Methods for spectrally resolving fluorophores of a sample and systems for same

ABSTRACT

Aspects of the present disclosure include methods for spectrally resolving light from fluorophores having overlapping fluorescence spectra in a sample. Methods according to certain embodiments include detecting light with a light detection system from a sample having a plurality of fluorophores having overlapping fluorescence spectra and spectrally resolving light from each fluorophore in the sample. In some embodiments, methods include estimating the abundance of one or more of the fluorophores in the sample, such as on a particle. In certain instances, methods include identifying the particle in the sample based on the abundance of each fluorophore and sorting the particle. Methods according to some embodiments includes spectrally resolving the light from each fluorophore by calculating a spectral unmixing matrix for the fluorescence spectra of each fluorophore. Systems and integrated circuit devices (e.g., a field programmable gate array) for practicing the subject methods are also provided.

CROSS-REFERENCE TO RELATED APPLICATION

This application is related to U.S. Provisional Patent Application Ser.No. 62/786,186 filed Dec. 28, 2018; U.S. Provisional Patent ApplicationSer. No. 62/803,975 filed Feb. 11, 2019 and U.S. Provisional PatentApplication Ser. No. 62/924,999 filed Oct. 23, 2019; the disclosures ofwhich applications are herein incorporated by reference.

INTRODUCTION

Flow-type particle sorting systems, such as sorting flow cytometers, areused to sort particles in a fluid sample based on at least one measuredcharacteristic of the particles. In a flow-type particle sorting system,particles, such as molecules, analyte-bound beads, or individual cells,in a fluid suspension are passed in a stream by a detection region inwhich a sensor detects particles contained in the stream of the type tobe sorted. The sensor, upon detecting a particle of the type to besorted, triggers a sorting mechanism that selectively isolates theparticle of interest.

Particle sensing typically is carried out by passing the fluid stream bya detection region in which the particles are exposed to irradiatinglight, from one or more lasers, and the light scattering andfluorescence properties of the particles are measured. Particles orcomponents thereof can be labeled with fluorescent dyes to facilitatedetection, and a multiplicity of different particles or components maybe simultaneously detected by using spectrally distinct fluorescent dyesto label the different particles or components. Detection is carried outusing one or more photosensors to facilitate the independent measurementof the fluorescence of each distinct fluorescent dye.

To sort particles in the sample, a drop charging mechanism chargesdroplets of the flow stream containing a particle type to be sorted withan electrical charge at the break-off point of the flow stream. Dropletsare passed through an electrostatic field and are deflected based onpolarity and magnitude of charge on the droplet into one or morecollection containers. Uncharged droplets are not deflected by theelectrostatic field.

SUMMARY

Aspects of the present disclosure include methods for spectrallyresolving light from fluorophores having overlapping fluorescencespectra in a sample. Methods according to certain embodiments includedetecting light with a light detection system from a sample having aplurality of fluorophores having overlapping fluorescence spectra andspectrally resolving light from each fluorophore in the sample. In someembodiments, methods include estimating the abundance of one or more ofthe fluorophores in the sample, such as on a particle. In certaininstances, methods include identifying the particle in the sample basedon the abundance of each fluorophore and sorting the particle. Methodsaccording to some embodiments include spectrally resolving the lightfrom each fluorophore by calculating a spectral unmixing matrix for thefluorescence spectra of each fluorophore. Systems and integrated circuitdevices (e.g., a field programmable gate array) for practicing thesubject methods are also provided.

In some embodiments, samples of interest include a plurality offluorophores where the fluorescence spectra of each fluorophore overlapswith the fluorescence spectra of at least one other fluorophore in thesample. In certain instances, the fluorescence spectra of eachfluorophore overlaps with the fluorescence spectra of at least one otherfluorophore in the sample by 10 nm or more, such as 25 nm or more andincluding by 50 nm or more. In some instances, the fluorescence spectraof one or more fluorophores in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample, such as by 10 nm ormore, such as by 25 nm or more and including by 50 nm or more. In otherembodiments, samples of interest include a plurality of fluorophoreshaving non-overlapping fluorescence spectra. In these embodiments, thefluorescence spectra of each fluorophore is adjacent to at least oneother fluorophore within 10 nm or less, such as 9 nm or less, such as 8nm or less, such as 7 nm or less, such as 6 nm or less, such as 5 nm orless, such as 4 nm or less, such as 3 nm or less, such as 2 nm or lessand including 1 nm or less.

In some embodiments, methods include spectrally resolving light fromeach fluorophore by calculating a spectral unmixing matrix for thefluorescence spectra of each fluorophore in the sample. In someinstances, calculating the spectral unmixing matrix includes using aweighted least square algorithm. In some instances, the weighted leastsquares algorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

where y is measured detector values from the plurality of photodetectorsof a light detection system for each particle (e.g., cell); â isestimated fluorophore abundance; X is spillover; and W is

$\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}.$

In some embodiments, each W_(ii) is calculated according to:

$W_{ii} = {\frac{1}{\sigma_{t}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

where σ_(i) ² is variance at detector i; y_(i) is signal at detector i;and λ_(i) is constant noise at detector i. In certain embodiments, thespectral unmixing matrix is calculated according to: (X^(T)WX)⁻¹X^(T)W.In some instances, (X^(T)WX) is inverted for each particle detected bythe light detection system to calculate a spectral unmixing matrix.

In certain embodiments, methods for spectrally resolving light from eachfluorophore include approximating the inversion of (X^(T)WX) in theweighted least square algorithm for each particle detected by the lightdetection system, such as for example in order to sort particles in thesample in real time. In some embodiments, inverting (X^(T)WX) includesapproximating (X^(T)WX)⁻¹ using an iterative Newton-Raphson calculationaccording to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

where W_(G) is a predetermined approximation of W that is determinedfrom baseline variance of each photodetector (i.e., in the absence offluorescence due to a particle) in the light detection system. In someembodiments, methods further include estimating the baseline variance ofeach photodetector. In some instances, methods include determining thephotodetector noise components (e.g., electronic noise, backgroundlight, etc.) using a single stain control sample. In certain instances,methods include determining the variance of each photodetector beforeirradiating the sample with the light source. In other instances,methods include determining the predetermined approximation of W, W_(G),before irradiating the sample with the light source. In certainembodiments, methods include precomputing A₀ ⁻¹ with the predeterminedW_(G). In these embodiments, the precomputed A₀ ⁻¹ can be used as afirst approximation of the A⁻¹ for each particle detected by the lightdetection system.

In other embodiments, methods for spectrally resolving light from eachfluorophore include using a Sherman-Morrison iterative inverse updater.In some instances, methods include computing A using theSherman-Morrison formula:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - \frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}}$

In certain instances, methods include precomputing A₀ ⁻¹ to compute theinverse of a perturbation of A₀ using the Sherman-Morrison formula. Insome embodiments, the inverse of A₀ is calculated by the formulaX^(T)W₀X and the inverse of A is calculated by the formula X^(T)WX. Insome instances, methods include calculating ΔA (i.e., A−A₀) as a productof column vectors with each iterative W according to:

$W_{0} = {{\begin{bmatrix}w_{11}^{0} & 0 & \ldots & 0 \\0 & w_{22}^{0} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}^{0}\end{bmatrix}\mspace{14mu}{and}\mspace{14mu} W} = \begin{bmatrix}w_{11} & 0 & \ldots & 0 \\0 & w_{22} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}\end{bmatrix}}$

-   -   where w_(ii)=w⁰ _(ii)+α_(i) for iϵ[1, N_(D)].

${W_{1} = {W_{0} + \begin{bmatrix}\alpha_{1} & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}},{W_{2} = {{W_{1} + \begin{bmatrix}0 & 0 & \ldots & 0 \\0 & \alpha_{2} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}❘\mspace{14mu}{and}}}$${W = {W_{N_{D}} = {W_{N_{D} - 1} + {\begin{bmatrix}0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \alpha_{N_{D}}\end{bmatrix}\mspace{14mu}{and}}}}}\mspace{11mu}$${\Delta\; W_{i}} = {{W_{i} - W} = \begin{bmatrix}0 & 0 & 0 & \ldots & 0 \\\vdots & \ddots & \vdots & \vdots & 0 \\0 & \ldots & \alpha_{i} & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & \ldots & 0\end{bmatrix}}$

According to embodiments, ΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) whereA can be expressed as:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

In these embodiments, each A can be recomputed from A₀ with each newweight matrix W (i.e., with different values from W₀) using the changeto each w_(i). In some embodiments, methods include performing aSherman-Morrison iterative inverse updater for approximating thespectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

In some embodiments, a precomputed value for A₀ ⁻¹ is used to calculateA₁ ⁻¹. The precomputed A₁ ⁻¹ is then used to calculate A₂ ⁻¹. The valueA⁻¹ can be calculated by repeat computing of A_(i) ⁻¹ using each(A_(i−1))⁻¹ from i=1 to N_(D).

In some embodiments, methods for spectrally resolving light from eachfluorophore include calculating a weighted least squares algorithm bymatrix decomposition (i.e., factorization). In some instances, methodsinclude LU matrix decomposition, such as where a matrix is decomposedinto a product of a lower-triangular (L) matrix and an upper-triangular(U) matrix. In certain instances, LU decomposition includes Gaussianelimination. In other instances, LU decomposition includes a modifiedCholesky decomposition, an LDL decomposition where D is diagonal matrix.In certain embodiments, the weighted least squares algorithm (a) iscalculated using a modified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B LDL decomposition

Lz=B where z=DL ^(T) a Lower-triangular matrix solution

Dx=z where x=L ^(T) a Diagonal matrix solution

L ^(T) a=x Upper-triangular matrix solution

In other embodiments, methods for spectrally resolving light from eachfluorophore include calculating a weighted least squares algorithm by QRfactorization. In some instances, the QR factorization is a matrix thatis the product of an orthogonal (Q) matrix and an upper-triangular (R)matrix. In some embodiments, the weighted least squares algorithm (a) iscalculated using QR factorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X (QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

In yet other embodiments, methods for spectrally resolving light fromeach fluorophore include calculating a weighted least squares algorithmby singular value decomposition (SVD). In some instances, the singularvalue decomposition is the matrix that is the product X=UΣV^(T) where Uand V are orthogonal matrices and Σ is a diagonal matrix containingsingular values of X In certain instances, the weighted least squaresalgorithm (a) is calculated using singular value decomposition accordingto:

z=U ^(T) y

Σw=z

a=Vw

In some embodiments, the abundance of one or more of fluorophores in thesample (e.g., on a particle) is determined by spectrally resolving thelight from each fluorophore. In some embodiments, spectrally resolvinglight from each fluorophore in the sample includes calculating aspectral unmixing matrix for the fluorescence spectra of eachfluorophore (e.g., on a target particle). In some instances, methodsinclude estimating the abundance of one or more fluorophores on aparticle and identifying the particle in the sample based on theestimated abundance of each fluorophore. In certain instances,identified particles (e.g., cells in a biological sample) in the sampleare sorted.

Systems for practicing the subject methods are also provided. Systemsaccording to certain embodiments include a light source configured toirradiate a sample having a plurality of fluorophores that haveoverlapping fluorescence spectra; a light detection system comprising aplurality of photodetectors; and a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor tospectrally resolve light from each fluorophore in the sample. In someembodiments, the processor includes memory with instructions which whenexecuted by the processor, cause the processor to spectrally resolvefluorescence from each fluorophore by calculating a spectral unmixingmatrix for the fluorescence spectra of each fluorophore in the sample.In some instances, the weighted least squares algorithm is calculatedaccording to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

where y is measured detector values from the plurality of photodetectorsof the light detection system for each particle; â is estimatedfluorophore abundance X is spillover; and W is

$\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}.$

In some embodiments, each W_(ii) is calculated according to:

$W_{ii} = {\frac{1}{\sigma_{t}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

where σ_(i) ² is variance at detector i; y_(i) is signal at detector i;and λ_(i) is constant noise at detector i. In certain embodiments, thespectral unmixing matrix is calculated according to: (X^(T)WX)⁻¹X^(T)W.In some instances, (X^(T)WX) is inverted for each particle detected bythe light detection system to calculate a spectral unmixing matrix.

In certain embodiments, systems include a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor toapproximate the inversion of (X^(T)WX) in the weighted least squarealgorithm for each particle detected by the light detection system inorder to sort particles in the sample in real time. In certaininstances, the inversion of (X^(T)WX) is approximated using an iterativeNewton-Raphson calculation according to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

where W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system. Thevariance, in some embodiments, has a photodetector noise component. Forexample, the photodetector noise component may include one or more ofelectronic noise and optical background light. In some embodiments, thevariance of the photodetector is proportional to measured intensity oflight by the photodetector. In some embodiments, the photodetector noisecomponent is estimated using a single stain control sample. In certainembodiments, the memory includes instructions stored thereon, which whenexecuted by the processor, cause the processor to automaticallydetermine the variance of each photodetector before irradiating thesample with the light source. In other embodiments, the memory includesinstructions stored thereon, which when executed by the processor, causethe processor to automatically predetermine W_(G) before irradiating thesample with the light source. In certain embodiments, the memoryincludes instructions stored thereon, which when executed by theprocessor, cause the processor to precompute A₀ ⁻¹ with thepredetermined W_(G). In these embodiments, the precomputed A₀ ⁻¹ may bestored in memory and used by the processor as a first approximation ofthe A⁻¹ for each particle detected by the light detection system.

In other embodiments, systems include a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor toapproximate the weighted least square algorithm for each particle with aSherman-Morrison iterative inverse updater. In some instances, thememory includes instructions for computing A using the Sherman-Morrisonformula:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - \frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}}$

In certain instances, the memory includes instructions for precomputingA₀ ⁻¹ to compute the inverse of a perturbation of A₀ using theSherman-Morrison formula. In some embodiments, the inverse of A₀ iscalculated by the formula X^(T)W₀X and the inverse of A is calculated bythe formula X^(T)WX. In some instances, the memory includes instructionsfor calculating ΔA (i.e., A−A₀) as a product of column vectors with eachiterative W according to:

$W_{0} = {{\begin{bmatrix}w_{11}^{0} & 0 & \ldots & 0 \\0 & w_{22}^{0} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}^{0}\end{bmatrix}\mspace{14mu}{and}\mspace{14mu} W} = \begin{bmatrix}w_{11} & 0 & \ldots & 0 \\0 & w_{22} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}\end{bmatrix}}$

-   -   where w_(ii)=w⁰ _(ii)+α_(i) for iϵ[1, N_(D)].

${W_{1} = {W_{0} + \begin{bmatrix}\alpha_{1} & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}},{W_{2} = {{W_{1} + \begin{bmatrix}0 & 0 & \ldots & 0 \\0 & \alpha_{2} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}❘\mspace{14mu}{and}}}$${W = {W_{N_{D}} = {W_{N_{D} - 1} + {\begin{bmatrix}0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \alpha_{N_{D}}\end{bmatrix}\mspace{14mu}{and}}}}}\mspace{11mu}$${\Delta\; W_{i}} = {{W_{i} - W} = \begin{bmatrix}0 & 0 & 0 & \ldots & 0 \\\vdots & \ddots & \vdots & \vdots & 0 \\0 & \ldots & \alpha_{i} & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & \ldots & 0\end{bmatrix}}$

According to embodiments, ΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) whereA can be expressed as:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

In these embodiments, each A can be recomputed from A₀ with each newweight matrix W (i.e., with different values from W₀) using the changeto each w_(i). In some embodiments, systems include a processor withmemory operably coupled to the processor where the memory includesinstructions stored thereon, which when executed by the processor, causethe processor to perform a Sherman-Morrison iterative inverse updaterfor approximating the spectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

In some embodiments, a precomputed value for A₀ ⁻¹ is used to calculateA₁ ⁻¹. The precomputed A₁ ⁻¹ is then used to calculate A₂ ⁻¹. The valueA⁻¹ can be calculated by repeat computing of A_(i) ⁻¹ using each(A_(i−1))⁻¹ from i=1 to N_(D).

In other embodiments, systems include a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor tocalculate the weighted least square algorithm for each particle bymatrix decomposition. In some instances, the memory includesinstructions for a LU matrix decomposition, such as where a matrix isdecomposed into a product of a lower-triangular (L) matrix and anupper-triangular (U) matrix. In certain instances, LU decompositionincludes Gaussian elimination. In other instances, LU decompositionincludes a modified Cholesky decomposition, an LDL decomposition where Dis diagonal matrix. In certain embodiments, systems include a processorwith memory operably coupled to the processor where the memory includesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm (a)using a modified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B LDL decomposition

Lz=B where z=DL ^(T) a Lower-triangular matrix solution

Dx=z where x=L ^(T) a Diagonal matrix solution

L ^(T) a=x Upper-triangular matrix solution

In other embodiments, systems include a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor tocalculate a weighted least squares algorithm by QR factorization. Insome instances, the QR factorization is a matrix that is the product ofan orthogonal (Q) matrix and an upper-triangular (R) matrix. In someembodiments, the memory includes instructions for calculating theweighted least squares algorithm (a) using QR factorization accordingto:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X (QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

In yet other embodiments, systems include a processor with memoryoperably coupled to the processor where the memory includes instructionsstored thereon, which when executed by the processor, cause theprocessor to calculate a weighted least squares algorithm by singularvalue decomposition (SVD). In some instances, the singular valuedecomposition is the matrix that is the product X=UΣV^(T) where U and Vare orthogonal matrices and Σ is a diagonal matrix containing singularvalues of X In certain instances, the memory includes instructions forcalculating the weighted least squares algorithm (a) using singularvalue decomposition according to:

z=U ^(T) y

Σw=z

a=Vw

In some embodiments, systems include a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor toestimate an abundance of one or more of the fluorophores in the samplebased the calculated spectral unmixing matrix. In certain instances, thememory includes instructions for estimating the abundance of one or morefluorophores on a particle in the sample. In some embodiments the memoryincludes instructions for identifying a particle in the sample based onthe estimated abundance of each fluorophore on the particle. In certaininstances, systems include a particle sorter for sorting identifiedparticles in the sample.

Integrated circuit devices programmed to spectrally resolve light from aplurality of fluorophores in a sample are also provided. In embodiments,the integrated circuit device may be a field programmable gated array(FPGA), an application specific integrated circuit (ASIC) or a complexprogrammable logic device (CPLD), or some other integrated circuitdevice. In some embodiments, the integrated circuit device is programmedto spectrally resolve fluorescence from each fluorophore by calculatinga spectral unmixing matrix for the fluorescence spectra of eachfluorophore in the sample. In some instances, the weighted least squaresalgorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

where y is measured detector values from the plurality of photodetectorsof the light detection system for each particle; a is estimatedfluorophore abundance X is spillover; and W is

$\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}.$

In some embodiments, each W_(ii) is calculated according to:

$W_{ii} = {\frac{1}{\sigma_{t}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

where σ_(i) ² is variance at detector i; y_(i) is signal at detector i;and λ_(i) is constant noise at detector i. In certain embodiments, thespectral unmixing matrix is calculated according to: (X^(T)WX)⁻¹X^(T)W.In some instances, (X^(T)WX) is inverted for each particle detected bythe light detection system to calculate a spectral unmixing matrix.

In certain embodiments, integrated circuit devices are programmed toapproximate the inversion of (X^(T)WX) in the weighted least squarealgorithm for each particle detected by the light detection system inorder to sort particles in the sample in real time. In certaininstances, the inversion of (X^(T)WX) is approximated using an iterativeNewton-Raphson calculation according to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

where W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system. Insome embodiments, the integrated circuit device is programmed to furtherestimate the variance of each photodetector. In certain instances, theintegrated circuit device is programmed with an estimate of thephotodetector noise components based on a single stain control sample.In other instances, the variance of each photodetector is programmedinto the integrated circuit device before the sample is irradiated witha light source. In still other instances, the predeterminedapproximation of Win the iterative Newton-Raphson calculation, W_(G), isprogrammed into the integrated circuit device before the sample isirradiated with a light source. In certain embodiments, the integratedcircuit device is programmed to precompute A₀ ⁻¹ with the predeterminedW_(G). In these embodiments, the precomputed A₀ ⁻¹ may be programmedinto the integrated circuit device and used as a first approximation ofthe A⁻¹ for each particle detected by the light detection system.

In other embodiments, integrated circuit devices of interest areprogrammed to approximate the weighted least square algorithm for eachparticle with a Sherman-Morrison iterative inverse updater. In someinstances, the integrated circuit device is programmed for computing Ausing the Sherman-Morrison formula:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - \frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}}$

In certain instances, the integrated circuit device is programmed forprecomputing A₀ ⁻¹ to compute the inverse of a perturbation of A₀ usingthe Sherman-Morrison formula. In some embodiments, the inverse of A₀ iscalculated by the formula X^(T)W₀X and the inverse of A is calculated bythe formula X^(T)WX. In some instances, the integrated circuit device isprogrammed to calculate ΔA (i.e., A−A₀) as a product of column vectorswith each iterative W according to:

$W_{0} = {{\begin{bmatrix}w_{11}^{0} & 0 & \ldots & 0 \\0 & w_{22}^{0} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}^{0}\end{bmatrix}\mspace{14mu}{and}\mspace{14mu} W} = \begin{bmatrix}w_{11} & 0 & \ldots & 0 \\0 & w_{22} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}\end{bmatrix}}$

-   -   where w_(ii)=w⁰ _(ii)+α_(i) for iϵ[1, N_(D)].

${W_{1} = {W_{0} + \begin{bmatrix}\alpha_{1} & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}},{W_{2} = {{W_{1} + \begin{bmatrix}0 & 0 & \ldots & 0 \\0 & \alpha_{2} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}❘\mspace{14mu}{and}}}$${W = {W_{N_{D}} = {W_{N_{D} - 1} + {\begin{bmatrix}0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \alpha_{N_{D}}\end{bmatrix}\mspace{14mu}{and}}}}}\mspace{11mu}$${\Delta\; W_{i}} = {{W_{i} - W} = \begin{bmatrix}0 & 0 & 0 & \ldots & 0 \\\vdots & \ddots & \vdots & \vdots & 0 \\0 & \ldots & \alpha_{i} & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & \ldots & 0\end{bmatrix}}$

According to embodiments, ΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) whereA can be expressed as:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

In these embodiments, each A can be recomputed from A₀ with each newweight matrix W (i.e., with different values from W₀) using the changeto each w_(i). In some embodiments, the integrated circuit device isprogrammed to perform a Sherman-Morrison iterative inverse updater forapproximating the spectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

In some embodiments, a precomputed value for A₀ ⁻¹ is used to calculateA₁ ⁻¹. The precomputed A₁ ⁻¹ is then used to calculate A₂ ⁻¹. The valueA⁻¹ can be calculated by repeat computing of A_(i) ⁻¹ using each(A_(i−1))⁻¹ from i=1 to N_(D).

In other embodiments, integrated circuit devices of interest areprogrammed to calculate the weighted least square algorithm for eachparticle by matrix decomposition. In some instances, the integratedcircuit device is programmed for instructions for a LU matrixdecomposition, such as where a matrix is decomposed into a product of alower-triangular (L) matrix and an upper-triangular (U) matrix. Incertain instances, LU decomposition includes Gaussian elimination. Inother instances, LU decomposition includes a modified Choleskydecomposition, an LDL decomposition where D is diagonal matrix. Incertain embodiments, integrated circuit devices are programmed tocalculate the weighted least squares algorithm (a) using a modifiedCholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B LDL decomposition

Lz=B where z=DL ^(T) a Lower-triangular matrix solution

Dx=z where x=L ^(T) a Diagonal matrix solution

L ^(T) a=x Upper-triangular matrix solution

In other embodiments, integrated circuit devices are programmed tocalculate a weighted least squares algorithm by QR factorization. Insome instances, the QR factorization is a matrix that is the product ofan orthogonal (Q) matrix and an upper-triangular (R) matrix. In someembodiments, integrated circuit devices are programmed to calculate theweighted least squares algorithm (a) using QR factorization accordingto:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X (QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

In yet other embodiments, integrated circuit devices are programmed tocalculate a weighted least squares algorithm by singular valuedecomposition (SVD). In some instances, the singular value decompositionis the matrix that is the product X=UΣV^(T) where U and V are orthogonalmatrices and Z is a diagonal matrix containing singular values of X Incertain instances, integrated circuit devices are programmed tocalculate the weighted least squares algorithm (a) using singular valuedecomposition according to:

z=U ^(T) y

Σw=z

a=Vw

In some embodiments, the integrated circuit devices are programmed toestimate an abundance of one or more of the fluorophores in the samplebased on the calculated spectral unmixing matrix. In certain instances,the integrated circuit device is programmed to estimate the abundance ofone or more fluorophores on a particle in the sample. In someembodiments, the integrated circuit devices are programmed to identify aparticle in the sample based on the estimated abundance of eachfluorophore on the particle. In certain instances, the integratedcircuit devices are programmed to sort the identified particles in thesample.

BRIEF DESCRIPTION OF THE FIGURES

The invention may be best understood from the following detaileddescription when read in conjunction with the accompanying drawings.Included in the drawings are the following figures:

FIG. 1 depicts a comparison of determining fluorophore abundance by a)traditional spectral overlap compensation; b) by spectral unmixingcalculated using an ordinary least squares algorithm; and c) by spectralunmixing calculated using a weighted least squares algorithm with aweight factor (W) that is approximated for each cell in real timeaccording to certain embodiments.

FIG. 2 depicts a comparison of spectral unmixing by a weighted leastsquares algorithm and approximation of the weight factor (W) to sortcells in real time according to certain embodiments.

DETAILED DESCRIPTION

Aspects of the present disclosure include methods for spectrallyresolving light from fluorophores having overlapping fluorescencespectra in a sample. Methods according to certain embodiments includedetecting light with a light detection system from a sample having aplurality of fluorophores having overlapping fluorescence spectra andspectrally resolving light from each fluorophore in the sample. In someembodiments, methods include estimating the abundance of one or more ofthe fluorophores in the sample, such as on a particle. In certaininstances, methods include identifying the particle in the sample basedon the abundance of each fluorophore and sorting the particle. Methodsaccording to some embodiments includes spectrally resolving the lightfrom each fluorophore by calculating a spectral unmixing matrix for thefluorescence spectra of each fluorophore. Systems and integrated circuitdevices (e.g., a field programmable gate array) for practicing thesubject methods are also provided.

Before the present invention is described in greater detail, it is to beunderstood that this invention is not limited to particular embodimentsdescribed, as such may, of course, vary. It is also to be understoodthat the terminology used herein is for the purpose of describingparticular embodiments only, and is not intended to be limiting, sincethe scope of the present invention will be limited only by the appendedclaims.

Where a range of values is provided, it is understood that eachintervening value, to the tenth of the unit of the lower limit unlessthe context clearly dictates otherwise, between the upper and lowerlimit of that range and any other stated or intervening value in thatstated range, is encompassed within the invention.

The upper and lower limits of these smaller ranges may independently beincluded in the smaller ranges and are also encompassed within theinvention, subject to any specifically excluded limit in the statedrange. Where the stated range includes one or both of the limits, rangesexcluding either or both of those included limits are also included inthe invention.

Certain ranges are presented herein with numerical values being precededby the term “about.” The term “about” is used herein to provide literalsupport for the exact number that it precedes, as well as a number thatis near to or approximately the number that the term precedes. Indetermining whether a number is near to or approximately a specificallyrecited number, the near or approximating unrecited number may be anumber which, in the context in which it is presented, provides thesubstantial equivalent of the specifically recited number.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Although any methods andmaterials similar or equivalent to those described herein can also beused in the practice or testing of the present invention, representativeillustrative methods and materials are now described.

All publications and patents cited in this specification are hereinincorporated by reference as if each individual publication or patentwere specifically and individually indicated to be incorporated byreference and are incorporated herein by reference to disclose anddescribe the methods and/or materials in connection with which thepublications are cited. The citation of any publication is for itsdisclosure prior to the filing date and should not be construed as anadmission that the present invention is not entitled to antedate suchpublication by virtue of prior invention. Further, the dates ofpublication provided may be different from the actual publication dateswhich may need to be independently confirmed.

It is noted that, as used herein and in the appended claims, thesingular forms “a”, “an”, and “the” include plural referents unless thecontext clearly dictates otherwise. It is further noted that the claimsmay be drafted to exclude any optional element. As such, this statementis intended to serve as antecedent basis for use of such exclusiveterminology as “solely,” “only” and the like in connection with therecitation of claim elements, or use of a “negative” limitation.

As will be apparent to those of skill in the art upon reading thisdisclosure, each of the individual embodiments described and illustratedherein has discrete components and features which may be readilyseparated from or combined with the features of any of the other severalembodiments without departing from the scope or spirit of the presentinvention. Any recited method can be carried out in the order of eventsrecited or in any other order which is logically possible.

While the apparatus and method has or will be described for the sake ofgrammatical fluidity with functional explanations, it is to be expresslyunderstood that the claims, unless expressly formulated under 35 U.S.C.§ 112, are not to be construed as necessarily limited in any way by theconstruction of “means” or “steps” limitations, but are to be accordedthe full scope of the meaning and equivalents of the definition providedby the claims under the judicial doctrine of equivalents, and in thecase where the claims are expressly formulated under 35 U.S.C. § 112 areto be accorded full statutory equivalents under 35 U.S.C. § 112.

As summarized above, the present disclosure provides methods forspectrally resolving fluorophores in a sample. In further describingembodiments of the disclosure, methods for spectrally resolvingfluorophores in a sample, including estimating an abundance of eachfluorophore in the sample (e.g., on a particle in the sample) as well asidentifying and sorting particles based on the estimated abundance ofeach fluorophore are first described in greater detail. Next, systemsand integrated circuited devices programmed to practice the subjectmethods, by calculating a spectral unmixing matrix, are described.

Methods for Spectrally Resolving Light from Fluorophores HavingOverlapping Fluorescence Spectra in a Sample

Aspects of the present disclosure include methods for spectrallyresolving light from fluorophores, including light having overlappingfluorescence spectra, in a sample. The term “spectrally resolving” isused herein in its conventional sense to refer to spectrallydistinguishing each fluorophore in the sample by assigning orattributing the overlapping wavelengths of light to each contributingfluorophore. In embodiments, the overlapping spectral component offluorescence that is attributed to each fluorophore is determined bycalculating a spectral unmixing matrix (as described in greater detailbelow). In some embodiments, samples of interest have a plurality offluorophores where the fluorescence spectra of each fluorophore overlapswith the fluorescence spectra of at least one other fluorophore in thesample. In some instances, the fluorescence spectra of each fluorophoreoverlaps with the fluorescence spectra of at least one other fluorophorein the sample by 5 nm or more, such as by 10 nm or more, such as by 25nm or more and including by 50 nm or more. In certain instances, thefluorescence spectra of one or more fluorophores in the sample overlapswith the fluorescence spectra of two or more different fluorophores inthe sample, such as where each overlap in fluorescence spectra is by 5nm or more, such as by 10 nm or more, such as by 25 nm or more andincluding by 50 nm or more. In other embodiments, samples of interestinclude a plurality of fluorophores having non-overlapping fluorescencespectra. In these embodiments, the fluorescence spectra of eachfluorophore is adjacent to at least one other fluorophore within 10 nmor less, such as 9 nm or less, such as 8 nm or less, such as 7 nm orless, such as 6 nm or less, such as 5 nm or less, such as 4 nm or less,such as 3 nm or less, such as 2 nm or less and including 1 nm or less.

In practicing the subject methods, a sample is irradiated with a lightsource and light from the sample is detected with a light detectionsystem having a plurality of photodetectors. In some embodiments, thesample is a biological sample. The term “biological sample” is used inits conventional sense to refer to a whole organism, plant, fungi or asubset of animal tissues, cells or component parts which may in certaininstances be found in blood, mucus, lymphatic fluid, synovial fluid,cerebrospinal fluid, saliva, bronchoalveolar lavage, amniotic fluid,amniotic cord blood, urine, vaginal fluid and semen. As such, a“biological sample” refers to both the native organism or a subset ofits tissues as well as to a homogenate, lysate or extract prepared fromthe organism or a subset of its tissues, including but not limited to,for example, plasma, serum, spinal fluid, lymph fluid, sections of theskin, respiratory, gastrointestinal, cardiovascular, and genitourinarytracts, tears, saliva, milk, blood cells, tumors, organs. Biologicalsamples may be any type of organismic tissue, including both healthy anddiseased tissue (e.g., cancerous, malignant, necrotic, etc.). In certainembodiments, the biological sample is a liquid sample, such as blood orderivative thereof, e.g., plasma, tears, urine, semen, etc., where insome instances the sample is a blood sample, including whole blood, suchas blood obtained from venipuncture or fingerstick (where the blood mayor may not be combined with any reagents prior to assay, such aspreservatives, anticoagulants, etc.).

In certain embodiments the source of the sample is a “mammal” or“mammalian”, where these terms are used broadly to describe organismswhich are within the class mammalia, including the orders carnivore(e.g., dogs and cats), rodentia (e.g., mice, guinea pigs, and rats), andprimates (e.g., humans, chimpanzees, and monkeys). In some instances,the subjects are humans. The methods may be applied to samples obtainedfrom human subjects of both genders and at any stage of development(i.e., neonates, infant, juvenile, adolescent, adult), where in certainembodiments the human subject is a juvenile, adolescent or adult. Whilethe present invention may be applied to samples from a human subject, itis to be understood that the methods may also be carried-out on samplesfrom other animal subjects (that is, in “non-human subjects”) such as,but not limited to, birds, mice, rats, dogs, cats, livestock and horses.

In practicing the subject methods, a sample (e.g., in a flow stream of aflow cytometer) is irradiated with light from a light source. In someembodiments, the light source is a broadband light source, emittinglight having a broad range of wavelengths, such as for example, spanning50 nm or more, such as 100 nm or more, such as 150 nm or more, such as200 nm or more, such as 250 nm or more, such as 300 nm or more, such as350 nm or more, such as 400 nm or more and including spanning 500 nm ormore. For example, one suitable broadband light source emits lighthaving wavelengths from 200 nm to 1500 nm. Another example of a suitablebroadband light source includes a light source that emits light havingwavelengths from 400 nm to 1000 nm. Where methods include irradiatingwith a broadband light source, broadband light source protocols ofinterest may include, but are not limited to, a halogen lamp, deuteriumarc lamp, xenon arc lamp, stabilized fiber-coupled broadband lightsource, a broadband LED with continuous spectrum, superluminescentemitting diode, semiconductor light emitting diode, wide spectrum LEDwhite light source, an multi-LED integrated white light source, amongother broadband light sources or any combination thereof.

In other embodiments, methods includes irradiating with a narrow bandlight source emitting a particular wavelength or a narrow range ofwavelengths, such as for example with a light source which emits lightin a narrow range of wavelengths like a range of 50 nm or less, such as40 nm or less, such as 30 nm or less, such as 25 nm or less, such as 20nm or less, such as 15 nm or less, such as 10 nm or less, such as 5 nmor less, such as 2 nm or less and including light sources which emit aspecific wavelength of light (i.e., monochromatic light). Where methodsinclude irradiating with a narrow band light source, narrow band lightsource protocols of interest may include, but are not limited to, anarrow wavelength LED, laser diode or a broadband light source coupledto one or more optical bandpass filters, diffraction gratings,monochromators or any combination thereof.

In certain embodiments, methods include irradiating the sample with oneor more lasers. As discussed above, the type and number of lasers willvary depending on the sample as well as desired light collected and maybe a gas laser, such as a helium-neon laser, argon laser, krypton laser,xenon laser, nitrogen laser, CO₂ laser, CO laser, argon-fluorine (ArF)excimer laser, krypton-fluorine (KrF) excimer laser, xenon chlorine(XeCl) excimer laser or xenon-fluorine (XeF) excimer laser or acombination thereof. In others instances, the methods includeirradiating the flow stream with a dye laser, such as a stilbene,coumarin or rhodamine laser. In yet other instances, methods includeirradiating the flow stream with a metal-vapor laser, such as ahelium-cadmium (HeCd) laser, helium-mercury (HeHg) laser,helium-selenium (HeSe) laser, helium-silver (HeAg) laser, strontiumlaser, neon-copper (NeCu) laser, copper laser or gold laser andcombinations thereof. In still other instances, methods includeirradiating the flow stream with a solid-state laser, such as a rubylaser, an Nd:YAG laser, NdCrYAG laser, Er:YAG laser, Nd:YLF laser,Nd:YVO₄ laser, Nd:YCa₄O(BO₃)₃ laser, Nd:YCOB laser, titanium sapphirelaser, thulim YAG laser, ytterbium YAG laser, ytterbium₂O₃ laser orcerium doped lasers and combinations thereof.

The sample may be irradiated with one or more of the above mentionedlight sources, such as 2 or more light sources, such as 3 or more lightsources, such as 4 or more light sources, such as 5 or more lightsources and including 10 or more light sources. The light source mayinclude any combination of types of light sources. For example, in someembodiments, the methods include irradiating the sample in the flowstream with an array of lasers, such as an array having one or more gaslasers, one or more dye lasers and one or more solid-state lasers.

The sample may be irradiated with wavelengths ranging from 200 nm to1500 nm, such as from 250 nm to 1250 nm, such as from 300 nm to 1000 nm,such as from 350 nm to 900 nm and including from 400 nm to 800 nm. Forexample, where the light source is a broadband light source, the samplemay be irradiated with wavelengths from 200 nm to 900 nm. In otherinstances, where the light source includes a plurality of narrow bandlight sources, the sample may be irradiated with specific wavelengths inthe range from 200 nm to 900 nm. For example, the light source may beplurality of narrow band LEDs (1 nm-25 nm) each independently emittinglight having a range of wavelengths between 200 nm to 900 nm. In otherembodiments, the narrow band light source includes one or more lasers(such as a laser array) and the sample is irradiated with specificwavelengths ranging from 200 nm to 700 nm, such as with a laser arrayhaving gas lasers, excimer lasers, dye lasers, metal vapor lasers andsolid-state laser as described above.

Where more than one light source is employed, the sample may beirradiated with the light sources simultaneously or sequentially, or acombination thereof. For example, the sample may be simultaneouslyirradiated with each of the light sources. In other embodiments, theflow stream is sequentially irradiated with each of the light sources.Where more than one light source is employed to irradiate the samplesequentially, the time each light source irradiates the sample mayindependently be 0.001 microseconds or more, such as 0.01 microsecondsor more, such as 0.1 microseconds or more, such as 1 microsecond ormore, such as 5 microseconds or more, such as 10 microseconds or more,such as 30 microseconds or more and including 60 microseconds or more.For example, methods may include irradiating the sample with the lightsource (e.g. laser) for a duration which ranges from 0.001 microsecondsto 100 microseconds, such as from 0.01 microseconds to 75 microseconds,such as from 0.1 microseconds to 50 microseconds, such as from 1microsecond to 25 microseconds and including from 5 microseconds to 10microseconds. In embodiments where sample is sequentially irradiatedwith two or more light sources, the duration sample is irradiated byeach light source may be the same or different.

The time period between irradiation by each light source may also vary,as desired, being separated independently by a delay of 0.001microseconds or more, such as 0.01 microseconds or more, such as 0.1microseconds or more, such as 1 microsecond or more, such as 5microseconds or more, such as by 10 microseconds or more, such as by 15microseconds or more, such as by 30 microseconds or more and includingby 60 microseconds or more. For example, the time period betweenirradiation by each light source may range from 0.001 microseconds to 60microseconds, such as from 0.01 microseconds to 50 microseconds, such asfrom 0.1 microseconds to 35 microseconds, such as from 1 microsecond to25 microseconds and including from 5 microseconds to 10 microseconds. Incertain embodiments, the time period between irradiation by each lightsource is 10 microseconds. In embodiments where sample is sequentiallyirradiated by more than two (i.e., 3 or more) light sources, the delaybetween irradiation by each light source may be the same or different.

The sample may be irradiated continuously or in discrete intervals. Insome instances, methods include irradiating the sample in the samplewith the light source continuously. In other instances, the sample in isirradiated with the light source in discrete intervals, such asirradiating every 0.001 millisecond, every 0.01 millisecond, every 0.1millisecond, every 1 millisecond, every 10 milliseconds, every 100milliseconds and including every 1000 milliseconds, or some otherinterval.

Depending on the light source, the sample may be irradiated from adistance which varies such as 0.01 mm or more, such as 0.05 mm or more,such as 0.1 mm or more, such as 0.5 mm or more, such as 1 mm or more,such as 2.5 mm or more, such as 5 mm or more, such as 10 mm or more,such as 15 mm or more, such as 25 mm or more and including 50 mm ormore. Also, the angle or irradiation may also vary, ranging from 10° to90°, such as from 15° to 85°, such as from 20° to 80°, such as from 25°to 75° and including from 30° to 60°, for example at a 90° angle.

In certain embodiments, methods include irradiating the sample with twoor more beams of frequency shifted light. As described above, a lightbeam generator component may be employed having a laser and anacousto-optic device for frequency shifting the laser light. In theseembodiments, methods include irradiating the acousto-optic device withthe laser. Depending on the desired wavelengths of light produced in theoutput laser beam (e.g., for use in irradiating a sample in a flowstream), the laser may have a specific wavelength that varies from 200nm to 1500 nm, such as from 250 nm to 1250 nm, such as from 300 nm to1000 nm, such as from 350 nm to 900 nm and including from 400 nm to 800nm. The acousto-optic device may be irradiated with one or more lasers,such as 2 or more lasers, such as 3 or more lasers, such as 4 or morelasers, such as 5 or more lasers and including 10 or more lasers. Thelasers may include any combination of types of lasers. For example, insome embodiments, the methods include irradiating the acousto-opticdevice with an array of lasers, such as an array having one or more gaslasers, one or more dye lasers and one or more solid-state lasers.

Where more than one laser is employed, the acousto-optic device may beirradiated with the lasers simultaneously or sequentially, or acombination thereof. For example, the acousto-optic device may besimultaneously irradiated with each of the lasers. In other embodiments,the acousto-optic device is sequentially irradiated with each of thelasers. Where more than one laser is employed to irradiate theacousto-optic device sequentially, the time each laser irradiates theacousto-optic device may independently be 0.001 microseconds or more,such as 0.01 microseconds or more, such as 0.1 microseconds or more,such as 1 microsecond or more, such as 5 microseconds or more, such as10 microseconds or more, such as 30 microseconds or more and including60 microseconds or more. For example, methods may include irradiatingthe acousto-optic device with the laser for a duration which ranges from0.001 microseconds to 100 microseconds, such as from 0.01 microsecondsto 75 microseconds, such as from 0.1 microseconds to 50 microseconds,such as from 1 microsecond to 25 microseconds and including from 5microseconds to 10 microseconds. In embodiments where the acousto-opticdevice is sequentially irradiated with two or more lasers, the durationthe acousto-optic device is irradiated by each laser may be the same ordifferent.

The time period between irradiation by each laser may also vary, asdesired, being separated independently by a delay of 0.001 microsecondsor more, such as 0.01 microseconds or more, such as 0.1 microseconds ormore, such as 1 microsecond or more, such as 5 microseconds or more,such as by 10 microseconds or more, such as by 15 microseconds or more,such as by 30 microseconds or more and including by 60 microseconds ormore. For example, the time period between irradiation by each lightsource may range from 0.001 microseconds to 60 microseconds, such asfrom 0.01 microseconds to 50 microseconds, such as from 0.1 microsecondsto 35 microseconds, such as from 1 microsecond to 25 microseconds andincluding from 5 microseconds to 10 microseconds. In certainembodiments, the time period between irradiation by each laser is 10microseconds. In embodiments where the acousto-optic device issequentially irradiated by more than two (i.e., 3 or more) lasers, thedelay between irradiation by each laser may be the same or different.

The acousto-optic device may be irradiated continuously or in discreteintervals. In some instances, methods include irradiating theacousto-optic device with the laser continuously. In other instances,the acousto-optic device is irradiated with the laser in discreteintervals, such as irradiating every 0.001 millisecond, every 0.01millisecond, every 0.1 millisecond, every 1 millisecond, every 10milliseconds, every 100 milliseconds and including every 1000milliseconds, or some other interval.

Depending on the laser, the acousto-optic device may be irradiated froma distance which varies such as 0.01 mm or more, such as 0.05 mm ormore, such as 0.1 mm or more, such as 0.5 mm or more, such as 1 mm ormore, such as 2.5 mm or more, such as 5 mm or more, such as 10 mm ormore, such as 15 mm or more, such as 25 mm or more and including 50 mmor more. Also, the angle or irradiation may also vary, ranging from 10°to 90°, such as from 15° to 85°, such as from 20° to 80°, such as from25° to 75° and including from 30° to 60°, for example at a 90° angle.

In embodiments, methods include applying radiofrequency drive signals tothe acousto-optic device to generate angularly deflected laser beams.Two or more radiofrequency drive signals may be applied to theacousto-optic device to generate an output laser beam with the desirednumber of angularly deflected laser beams, such as 3 or moreradiofrequency drive signals, such as 4 or more radiofrequency drivesignals, such as 5 or more radiofrequency drive signals, such as 6 ormore radiofrequency drive signals, such as 7 or more radiofrequencydrive signals, such as 8 or more radiofrequency drive signals, such as 9or more radiofrequency drive signals, such as 10 or more radiofrequencydrive signals, such as 15 or more radiofrequency drive signals, such as25 or more radiofrequency drive signals, such as 50 or moreradiofrequency drive signals and including 100 or more radiofrequencydrive signals.

The angularly deflected laser beams produced by the radiofrequency drivesignals each have an intensity based on the amplitude of the appliedradiofrequency drive signal. In some embodiments, methods includeapplying radiofrequency drive signals having amplitudes sufficient toproduce angularly deflected laser beams with a desired intensity. Insome instances, each applied radiofrequency drive signal independentlyhas an amplitude from about 0.001 V to about 500 V, such as from about0.005 V to about 400 V, such as from about 0.01 V to about 300 V, suchas from about 0.05 V to about 200 V, such as from about 0.1 V to about100 V, such as from about 0.5 V to about 75 V, such as from about 1 V to50 V, such as from about 2 V to 40 V, such as from 3 V to about 30 V andincluding from about 5 V to about 25 V. Each applied radiofrequencydrive signal has, in some embodiments, a frequency of from about 0.001MHz to about 500 MHz, such as from about 0.005 MHz to about 400 MHz,such as from about 0.01 MHz to about 300 MHz, such as from about 0.05MHz to about 200 MHz, such as from about 0.1 MHz to about 100 MHz, suchas from about 0.5 MHz to about 90 MHz, such as from about 1 MHz to about75 MHz, such as from about 2 MHz to about 70 MHz, such as from about 3MHz to about 65 MHz, such as from about 4 MHz to about 60 MHz andincluding from about 5 MHz to about 50 MHz.

In these embodiments, the angularly deflected laser beams in the outputlaser beam are spatially separated. Depending on the appliedradiofrequency drive signals and desired irradiation profile of theoutput laser beam, the angularly deflected laser beams may be separatedby 0.001 μm or more, such as by 0.005 μm or more, such as by 0.01 μm ormore, such as by 0.05 μm or more, such as by 0.1 μm or more, such as by0.5 μm or more, such as by 1 μm or more, such as by 5 μm or more, suchas by 10 μm or more, such as by 100 μm or more, such as by 500 μm ormore, such as by 1000 μm or more and including by 5000 μm or more. Insome embodiments, the angularly deflected laser beams overlap, such aswith an adjacent angularly deflected laser beam along a horizontal axisof the output laser beam. The overlap between adjacent angularlydeflected laser beams (such as overlap of beam spots) may be an overlapof 0.001 μm or more, such as an overlap of 0.005 μm or more, such as anoverlap of 0.01 μm or more, such as an overlap of 0.05 μm or more, suchas an overlap of 0.1 μm or more, such as an overlap of 0.5 μm or more,such as an overlap of 1 μm or more, such as an overlap of 5 μm or more,such as an overlap of 10 μm or more and including an overlap of 100 μmor more.

In certain instances, the flow stream is irradiated with a plurality ofbeams of frequency-shifted light and a cell in the flow stream is imagedby fluorescence imaging using radiofrequency tagged emission (FIRE) togenerate a frequency-encoded image, such as those described in Diebold,et al. Nature Photonics Vol. 7(10); 806-810 (2013) as well as describedin U.S. Pat. Nos. 9,423,353; 9,784,661 and 10,006,852 and U.S. PatentPublication Nos. 2017/0133857 and 2017/0350803, the disclosures of whichare herein incorporated by reference.

As discussed above, in embodiments light from the irradiated sample isconveyed to a light detection system as described in greater detailbelow and measured by the plurality of photodetectors. In someembodiments, methods include measuring the collected light over a rangeof wavelengths (e.g., 200 nm-1000 nm). For example, methods may includecollecting spectra of light over one or more of the wavelength ranges of200 nm-1000 nm. In yet other embodiments, methods include measuringcollected light at one or more specific wavelengths. For example, thecollected light may be measured at one or more of 450 nm, 518 nm, 519nm, 561 nm, 578 nm, 605 nm, 607 nm, 625 nm, 650 nm, 660 nm, 667 nm, 670nm, 668 nm, 695 nm, 710 nm, 723 nm, 780 nm, 785 nm, 647 nm, 617 nm andany combinations thereof. In certain embodiments, methods includingmeasuring wavelengths of light which correspond to the fluorescence peakwavelength of fluorophores. In some embodiments, methods includemeasuring collected light across the entire fluorescence spectrum ofeach fluorophore in the sample.

The collected light may be measured continuously or in discreteintervals. In some instances, methods include taking measurements of thelight continuously. In other instances, the light is measured indiscrete intervals, such as measuring light every 0.001 millisecond,every 0.01 millisecond, every 0.1 millisecond, every 1 millisecond,every 10 milliseconds, every 100 milliseconds and including every 1000milliseconds, or some other interval.

Measurements of the collected light may be taken one or more timesduring the subject methods, such as 2 or more times, such as 3 or moretimes, such as 5 or more times and including 10 or more times. Incertain embodiments, the light propagation is measured 2 or more times,with the data in certain instances being averaged.

Light from the sample may be measured at one or more wavelengths of,such as at 5 or more different wavelengths, such as at 10 or moredifferent wavelengths, such as at 25 or more different wavelengths, suchas at 50 or more different wavelengths, such as at 100 or more differentwavelengths, such as at 200 or more different wavelengths, such as at300 or more different wavelengths and including measuring the collectedlight at 400 or more different wavelengths.

In embodiments, methods include spectrally resolving the light from eachfluorophore in the sample. In some embodiments, the overlap between eachdifferent fluorophore is determined and the contribution of eachfluorophore to the overlapping fluorescence is calculated. In someembodiments, spectrally resolving light from each fluorophore includescalculating a spectral unmixing matrix for the fluorescence spectra foreach of the plurality of fluorophores having overlapping fluorescence inthe sample detected by the light detection system. As described ingreater detail below, spectrally resolving the light from eachfluorophore and calculating a spectral unmixing matrix for eachfluorophore may be used to estimate the abundance of each fluorophore inthe sample. In certain embodiments, the abundance of each fluorophoreassociated with a target particle may be determined. The abundance ofeach fluorophore associated with a target particle may be used inidentifying and classifying a particle. In some instances, identified orclassified particles may be used to sort target particles (e.g., cells)in the sample. In certain embodiments, spectrally resolving fluorophoresin the sample, such as by calculating spectral unmixing, is conducted sothat sorting is sufficiently fast to sort particles in real time afterdetection by the light detection system.

In some embodiments, spectrally resolving light from each fluorophorehaving overlapping fluorescence includes calculating the spectralunmixing matrix using a weighted least squares algorithm. In someinstances, the weighted least squares algorithm is calculated accordingto:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

where y is measured detector values from the plurality of photodetectorsof the light detection system for each cell: â is estimated fluorophoreabundance X is spillover; and W is

$\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}.$

In some embodiments, each W_(ii) is calculated according to:

$W_{ii} = {\frac{1}{\sigma_{t}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

where σ_(i) ² is variance at detector i; y_(i) is signal at detector i;and λ_(i) is constant noise at detector i. In certain embodiments, thespectral unmixing matrix is calculated according to: (X^(T)WX)⁻¹X^(T)W.In some instances, the method comprises inverting (X^(T)WX) for eachcell detected by the light detection system to calculate a spectralunmixing matrix.

In certain embodiments, methods include approximating the inversion of(X^(T)WX) in the weighted least square algorithm for each cell detectedby the light detection system. In some embodiments, inverting (X^(T)WX)includes approximating (X^(T)WX) using an iterative Newton-Raphsoncalculation according to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

where W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system. Insome embodiments, methods further include estimating the variance ofeach photodetector. In some instances, methods include determining thephotodetector noise components (e.g., electronic noise, backgroundlight, etc.) using a single stain control sample. In certain instances,methods include determining the variance of each photodetector beforeirradiating the sample with the light source. In other instances,methods include determining the predetermined approximation of W, W_(G),before irradiating the sample with the light source. In certainembodiments, methods include precomputing A₀ ⁻¹ with the predeterminedW_(G). In these embodiments, the precomputed A₀ ⁻¹ can be used as afirst approximation of the A⁻¹ for each particle detected by the lightdetection system.

In other embodiments, methods for spectrally resolving light from eachfluorophore include using a Sherman-Morrison iterative inverse updater.In some instances, methods include computing A using theSherman-Morrison formula:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - \frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}}$

In certain instances, methods include precomputing A₀ ⁻¹ to compute theinverse of a perturbation of A₀ using the Sherman-Morrison formula. Insome embodiments, the inverse of A₀ is calculated by the formulaX^(T)W₀X and the inverse of A is calculated by the formula X^(T)WX. Insome instances, methods include calculating ΔA (i.e., A−A₀) as a productof column vectors with each iterative W according to:

$W_{0} = {{\begin{bmatrix}w_{11}^{0} & 0 & \ldots & 0 \\0 & w_{22}^{0} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}^{0}\end{bmatrix}\mspace{14mu}{and}\mspace{14mu} W} = \begin{bmatrix}w_{11} & 0 & \ldots & 0 \\0 & w_{22} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}\end{bmatrix}}$

-   -   where w_(ii)=w⁰ _(ii)+α_(i) for iϵ[1, N_(D)].

${W_{1} = {W_{0} + \begin{bmatrix}\alpha_{1} & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}},{W_{2} = {{W_{1} + \begin{bmatrix}0 & 0 & \ldots & 0 \\0 & \alpha_{2} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}\; ❘\mspace{11mu}{and}}}$${W = {W_{N_{D}} = {W_{N_{D} - 1} + {\begin{bmatrix}0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \alpha_{N_{D}}\end{bmatrix}\mspace{14mu}{and}}}}}\mspace{11mu}$${\Delta\; W_{i}} = {{W_{i} - W} = \begin{bmatrix}0 & 0 & 0 & \ldots & 0 \\\vdots & \ddots & \vdots & \vdots & 0 \\0 & \ldots & \alpha_{i} & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & \ldots & 0\end{bmatrix}}$

According to embodiments, ΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) whereA can be expressed as:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

In these embodiments, each A can be recomputed from A₀ with each newweight matrix W (i.e., with different values from W₀) using the changeto each w_(i). In some embodiments, methods include performing aSherman-Morrison iterative inverse updater for approximating thespectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

In some embodiments, a precomputed value for A₀ ⁻¹ is used to calculateA₁ ⁻¹. The precomputed A₁ ⁻¹ is then used to calculate A₂ ⁻¹. The valueA⁻¹ can be calculated by repeat computing of A_(i) ⁻¹ using each(A_(i−1))⁻¹ from i=1 to N_(D).

In some embodiments, methods for spectrally resolving light from eachfluorophore include calculating a weighted least squares algorithm bymatrix decomposition (i.e., factorization). In some instances, methodsinclude LU matrix decomposition, such as where a matrix is decomposedinto a product of a lower-triangular (L) matrix and an upper-triangular(U) matrix. In certain instances, LU decomposition includes Gaussianelimination. In other instances, LU decomposition includes a modifiedCholesky decomposition, an LDL decomposition where D is diagonal matrix.In certain embodiments, the weighted least squares algorithm (a) iscalculated using a modified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B LDL decomposition

Lz=B where z=DL ^(T) a Lower-triangular matrix solution

Dx=z where x=L ^(T) a Diagonal matrix solution

L ^(T) a=x Upper-triangular matrix solution

In other embodiments, methods for spectrally resolving light from eachfluorophore include calculating a weighted least squares algorithm by QRfactorization. In some instances, the QR factorization is a matrix thatis the product of an orthogonal (Q) matrix and an upper-triangular (R)matrix. In some embodiments, the weighted least squares algorithm (a) iscalculated using QR factorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X (QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

In yet other embodiments, methods for spectrally resolving light fromeach fluorophore include calculating a weighted least squares algorithmby singular value decomposition (SVD). In some instances, the singularvalue decomposition is the matrix that is the product X=UΣV^(T) where Uand V are orthogonal matrices and Z is a diagonal matrix containingsingular values of X In certain instances, the weighted least squaresalgorithm (a) is calculated using singular value decomposition accordingto:

z=U ^(T) y

Σw=z

a=Vw

In some embodiments, methods include calculating the abundance of one ormore fluorophores in the sample from the spectrally resolved light fromeach fluorophore. In certain instances, the abundance of fluorophoresassociated with (e.g., chemically associated (i.e., covalently,ionically) or physically associated) a target particle is calculatedfrom the spectrally resolved light from each fluorophore associated withthe particle. For instance, in one example the relative abundance ofeach fluorophore associated with a target particle is calculated fromthe spectrally resolved light from each fluorophore. In another example,the absolute abundance of each fluorophore associated with the targetparticle is calculated from the spectrally resolved light from eachfluorophore. In certain embodiments, a particle may be identified orclassified based on the relative abundance of each fluorophoredetermined to be associated with the particle. In these embodiments, theparticle may be identified or classified by any convenient protocol suchas by: comparing the relative or absolute abundance of each fluorophoreassociated with a particle with a control sample having particles ofknown identity; or by conducting spectroscopic or other assay analysisof a population of particles (e.g., cells) having the calculatedrelative or absolute abundance of associated fluorophores.

In certain embodiments, methods include sorting one or more of theparticles (e.g., cells) of the sample that are identified based on theestimated abundance of the fluorophores associated with the particle.The term “sorting” is used herein in its conventional sense to refer toseparating components (e.g., droplets containing cells, dropletscontaining non-cellular particles such as biological macromolecules) ofa sample and in some instances, delivering the separated components toone or more sample collection containers. For example, methods mayinclude sorting 2 or more components of the sample, such as 3 or morecomponents, such as 4 or more components, such as 5 or more components,such as 10 or more components, such as 15 or more components andincluding sorting 25 or more components of the sample.

In sorting particles identified based on the abundance of fluorophoresassociated with the particle, methods include data acquisition, analysisand recording, such as with a computer, where multiple data channelsrecord data from each detector used in obtaining the overlapping spectraof the plurality of fluorophores associated with the particle. In theseembodiments, analysis includes spectrally resolving light (e.g., bycalculating the spectral unmixing matrix) from the plurality offluorophores having overlapping spectra that are associated with theparticle and identifying the particle based on the estimated abundanceof each fluorophore associated with the particle. This analysis may beconveyed to a sorting system which is configured to generate a set ofdigitized parameters based on the particle classification.

In some embodiments, methods for sorting components of sample includesorting particles (e.g., cells in a biological sample) with a particlesorting module having deflector plates, such as described in U.S. PatentPublication No. 2017/0299493, filed on Mar. 28, 2017, the disclosure ofwhich is incorporated herein by reference. In certain embodiments, cellsof the sample are sorted using a sort decision module having a pluralityof sort decision units, such as those described in U.S. ProvisionalPatent Application No. 62/803,264, filed on Feb. 8, 2019, the disclosureof which is incorporated herein by reference.

Systems for Spectrally Resolving Light from Fluorophores HavingOverlapping Fluorescence Spectra in a Sample

As summarized above, aspects of the present disclosure include a systemfor spectrally resolving light from fluorophores having overlappingfluorescence spectra in a sample. As described above, the term“spectrally resolving” is used herein in its conventional sense to referto spectrally distinguishing each fluorophore in the sample by assigningor attributing the overlapping wavelengths of light to each contributingfluorophore. In embodiments, the overlapping spectral component offluorescence that is attributed to each fluorophore is determined bycalculating a spectral unmixing matrix. In embodiments, the subjectsystems are used to characterize samples having a plurality offluorophores where the fluorescence spectra of each fluorophore overlapswith the fluorescence spectra of at least one other fluorophore in thesample. In some instances, the fluorescence spectra of each fluorophoreoverlaps with the fluorescence spectra of at least one other fluorophorein the sample by 5 nm or more, such as by 10 nm or more, such as by 25nm or more and including by 50 nm or more. In certain instances, thefluorescence spectra of one or more fluorophores in the sample overlapswith the fluorescence spectra of two or more different fluorophores inthe sample, such as where each overlap in fluorescence spectra is by 5nm or more, such as by 10 nm or more, such as by 25 nm or more andincluding by 50 nm or more. In embodiments, systems include a lightsource configured to irradiate a sample having a plurality offluorophores where the fluorescence spectra of each fluorophore overlapswith the fluorescence spectra of at least one other fluorophore in thesample. In embodiments, the light source may be any suitable broadbandor narrow band source of light. Depending on the components in thesample (e.g., cells, beads, non-cellular particles, etc.), the lightsource may be configured to emit wavelengths of light that vary, rangingfrom 200 nm to 1500 nm, such as from 250 nm to 1250 nm, such as from 300nm to 1000 nm, such as from 350 nm to 900 nm and including from 400 nmto 800 nm. For example, the light source may include a broadband lightsource emitting light having wavelengths from 200 nm to 900 nm. In otherinstances, the light source includes a narrow band light source emittinga wavelength ranging from 200 nm to 900 nm. For example, the lightsource may be a narrow band LED (1 nm-25 nm) emitting light having awavelength ranging between 200 nm to 900 nm. In certain embodiments, thelight source is a laser. In some instances, the subject systems includea gas laser, such as a helium-neon laser, argon laser, krypton laser,xenon laser, nitrogen laser, CO₂ laser, CO laser, argon-fluorine (ArF)excimer laser, krypton-fluorine (KrF) excimer laser, xenon chlorine(XeCl) excimer laser or xenon-fluorine (XeF) excimer laser or acombination thereof. In others instances, the subject systems include adye laser, such as a stilbene, coumarin or rhodamine laser. In yet otherinstances, lasers of interest include a metal-vapor laser, such as ahelium-cadmium (HeCd) laser, helium-mercury (HeHg) laser,helium-selenium (HeSe) laser, helium-silver (HeAg) laser, strontiumlaser, neon-copper (NeCu) laser, copper laser or gold laser andcombinations thereof. In still other instances, the subject systemsinclude a solid-state laser, such as a ruby laser, an Nd:YAG laser,NdCrYAG laser, Er:YAG laser, Nd:YLF laser, Nd:YVO₄ laser, Nd:YCa₄O(BO₃)₃laser, Nd:YCOB laser, titanium sapphire laser, thulim YAG laser,ytterbium YAG laser, ytterbium₂O₃ laser or cerium doped lasers andcombinations thereof.

In other embodiments, the light source is a non-laser light source, suchas a lamp, including but not limited to a halogen lamp, deuterium arclamp, xenon arc lamp, a light-emitting diode, such as a broadband LEDwith continuous spectrum, superluminescent emitting diode, semiconductorlight emitting diode, wide spectrum LED white light source, an multi-LEDintegrated. In some instances, the non-laser light source is astabilized fiber-coupled broadband light source, white light source,among other light sources or any combination thereof.

The light source may be positioned any suitable distance from the sample(e.g., the flow stream in a flow cytometer), such as at a distance of0.001 mm or more from the flow stream, such as 0.005 mm or more, such as0.01 mm or more, such as 0.05 mm or more, such as 0.1 mm or more, suchas 0.5 mm or more, such as 1 mm or more, such as 5 mm or more, such as10 mm or more, such as 25 mm or more and including at a distance of 100mm or more. In addition, the light source irradiate the sample at anysuitable angle (e.g., relative the vertical axis of the flow stream),such as at an angle ranging from 10° to 90°, such as from 15° to 85°,such as from 20° to 80°, such as from 25° to 75° and including from 30°to 60°, for example at a 90° angle.

The light source may be configured to irradiate the sample continuouslyor in discrete intervals. In some instances, systems include a lightsource that is configured to irradiate the sample continuously, such aswith a continuous wave laser that continuously irradiates the flowstream at the interrogation point in a flow cytometer. In otherinstances, systems of interest include a light source that is configuredto irradiate the sample at discrete intervals, such as every 0.001milliseconds, every 0.01 milliseconds, every 0.1 milliseconds, every 1millisecond, every 10 milliseconds, every 100 milliseconds and includingevery 1000 milliseconds, or some other interval. Where the light sourceis configured to irradiate the sample at discrete intervals, systems mayinclude one or more additional components to provide for intermittentirradiation of the sample with the light source. For example, thesubject systems in these embodiments may include one or more laser beamchoppers, manually or computer controlled beam stops for blocking andexposing the sample to the light source.

In some embodiments, the light source is a laser. Lasers of interest mayinclude pulsed lasers or continuous wave lasers. For example, the lasermay be a gas laser, such as a helium-neon laser, argon laser, kryptonlaser, xenon laser, nitrogen laser, CO₂ laser, CO laser, argon-fluorine(ArF) excimer laser, krypton-fluorine (KrF) excimer laser, xenonchlorine (XeCl) excimer laser or xenon-fluorine (XeF) excimer laser or acombination thereof; a dye laser, such as a stilbene, coumarin orrhodamine laser; a metal-vapor laser, such as a helium-cadmium (HeCd)laser, helium-mercury (HeHg) laser, helium-selenium (HeSe) laser,helium-silver (HeAg) laser, strontium laser, neon-copper (NeCu) laser,copper laser or gold laser and combinations thereof; a solid-statelaser, such as a ruby laser, an Nd:YAG laser, NdCrYAG laser, Er:YAGlaser, Nd:YLF laser, Nd:YVO₄ laser, Nd:YCa₄O(BO₃)₃ laser, Nd:YCOB laser,titanium sapphire laser, thulim YAG laser, ytterbium YAG laser,ytterbium₂O₃ laser or cerium doped lasers and combinations thereof; asemiconductor diode laser, optically pumped semiconductor laser (OPSL),or a frequency doubled- or frequency tripled implementation of any ofthe above mentioned lasers.

In certain embodiments, the light source is a light beam generator thatis configured to generate two or more beams of frequency shifted light.In some instances, the light beam generator includes a laser, aradiofrequency generator configured to apply radiofrequency drivesignals to an acousto-optic device to generate two or more angularlydeflected laser beams. In these embodiments, the laser may be a pulsedlasers or continuous wave laser. For example lasers in light beamgenerators of interest may be a gas laser, such as a helium-neon laser,argon laser, krypton laser, xenon laser, nitrogen laser, CO₂ laser, COlaser, argon-fluorine (ArF) excimer laser, krypton-fluorine (KrF)excimer laser, xenon chlorine (XeCl) excimer laser or xenon-fluorine(XeF) excimer laser or a combination thereof; a dye laser, such as astilbene, coumarin or rhodamine laser; a metal-vapor laser, such as ahelium-cadmium (HeCd) laser, helium-mercury (HeHg) laser,helium-selenium (HeSe) laser, helium-silver (HeAg) laser, strontiumlaser, neon-copper (NeCu) laser, copper laser or gold laser andcombinations thereof; a solid-state laser, such as a ruby laser, anNd:YAG laser, NdCrYAG laser, Er:YAG laser, Nd:YLF laser, Nd:YVO4 laser,Nd:YCa4O(BO3)3 laser, Nd:YCOB laser, titanium sapphire laser, thulim YAGlaser, ytterbium YAG laser, ytterbium2O3 laser or cerium doped lasersand combinations thereof.

The acousto-optic device may be any convenient acousto-optic protocolconfigured to frequency shift laser light using applied acoustic waves.In certain embodiments, the acousto-optic device is an acousto-opticdeflector. The acousto-optic device in the subject system is configuredto generate angularly deflected laser beams from the light from thelaser and the applied radiofrequency drive signals. The radiofrequencydrive signals may be applied to the acousto-optic device with anysuitable radiofrequency drive signal source, such as a direct digitalsynthesizer (DDS), arbitrary waveform generator (AWG), or electricalpulse generator.

In embodiments, a controller is configured to apply radiofrequency drivesignals to the acousto-optic device to produce the desired number ofangularly deflected laser beams in the output laser beam, such as beingconfigured to apply 3 or more radiofrequency drive signals, such as 4 ormore radiofrequency drive signals, such as 5 or more radiofrequencydrive signals, such as 6 or more radiofrequency drive signals, such as 7or more radiofrequency drive signals, such as 8 or more radiofrequencydrive signals, such as 9 or more radiofrequency drive signals, such as10 or more radiofrequency drive signals, such as 15 or moreradiofrequency drive signals, such as 25 or more radiofrequency drivesignals, such as 50 or more radiofrequency drive signals and includingbeing configured to apply 100 or more radiofrequency drive signals.

In some instances, to produce an intensity profile of the angularlydeflected laser beams in the output laser beam, the controller isconfigured to apply radiofrequency drive signals having an amplitudethat varies such as from about 0.001 V to about 500 V, such as fromabout 0.005 V to about 400 V, such as from about 0.01 V to about 300 V,such as from about 0.05 V to about 200 V, such as from about 0.1 V toabout 100 V, such as from about 0.5 V to about 75 V, such as from about1 V to 50 V, such as from about 2 V to 40 V, such as from 3 V to about30 V and including from about 5 V to about 25 V. Each appliedradiofrequency drive signal has, in some embodiments, a frequency offrom about 0.001 MHz to about 500 MHz, such as from about 0.005 MHz toabout 400 MHz, such as from about 0.01 MHz to about 300 MHz, such asfrom about 0.05 MHz to about 200 MHz, such as from about 0.1 MHz toabout 100 MHz, such as from about 0.5 MHz to about 90 MHz, such as fromabout 1 MHz to about 75 MHz, such as from about 2 MHz to about 70 MHz,such as from about 3 MHz to about 65 MHz, such as from about 4 MHz toabout 60 MHz and including from about 5 MHz to about 50 MHz.

In certain embodiments, the controller has a processor having memoryoperably coupled to the processor such that the memory includesinstructions stored thereon, which when executed by the processor, causethe processor to produce an output laser beam with angularly deflectedlaser beams having a desired intensity profile. For example, the memorymay include instructions to produce two or more angularly deflectedlaser beams with the same intensities, such as 3 or more, such as 4 ormore, such as 5 or more, such as 10 or more, such as 25 or more, such as50 or more and including memory may include instructions to produce 100or more angularly deflected laser beams with the same intensities. Inother embodiments, the may include instructions to produce two or moreangularly deflected laser beams with different intensities, such as 3 ormore, such as 4 or more, such as 5 or more, such as 10 or more, such as25 or more, such as 50 or more and including memory may includeinstructions to produce 100 or more angularly deflected laser beams withdifferent intensities.

In certain embodiments, the controller has a processor having memoryoperably coupled to the processor such that the memory includesinstructions stored thereon, which when executed by the processor, causethe processor to produce an output laser beam having increasingintensity from the edges to the center of the output laser beam alongthe horizontal axis. In these instances, the intensity of the angularlydeflected laser beam at the center of the output beam may range from0.1% to about 99% of the intensity of the angularly deflected laserbeams at the edge of the output laser beam along the horizontal axis,such as from 0.5% to about 95%, such as from 1% to about 90%, such asfrom about 2% to about 85%, such as from about 3% to about 80%, such asfrom about 4% to about 75%, such as from about 5% to about 70%, such asfrom about 6% to about 65%, such as from about 7% to about 60%, such asfrom about 8% to about 55% and including from about 10% to about 50% ofthe intensity of the angularly deflected laser beams at the edge of theoutput laser beam along the horizontal axis. In other embodiments, thecontroller has a processor having memory operably coupled to theprocessor such that the memory includes instructions stored thereon,which when executed by the processor, cause the processor to produce anoutput laser beam having an increasing intensity from the edges to thecenter of the output laser beam along the horizontal axis. In theseinstances, the intensity of the angularly deflected laser beam at theedges of the output beam may range from 0.1% to about 99% of theintensity of the angularly deflected laser beams at the center of theoutput laser beam along the horizontal axis, such as from 0.5% to about95%, such as from 1% to about 90%, such as from about 2% to about 85%,such as from about 3% to about 80%, such as from about 4% to about 75%,such as from about 5% to about 70%, such as from about 6% to about 65%,such as from about 7% to about 60%, such as from about 8% to about 55%and including from about 10% to about 50% of the intensity of theangularly deflected laser beams at the center of the output laser beamalong the horizontal axis. In yet other embodiments, the controller hasa processor having memory operably coupled to the processor such thatthe memory includes instructions stored thereon, which when executed bythe processor, cause the processor to produce an output laser beamhaving an intensity profile with a Gaussian distribution along thehorizontal axis. In still other embodiments, the controller has aprocessor having memory operably coupled to the processor such that thememory includes instructions stored thereon, which when executed by theprocessor, cause the processor to produce an output laser beam having atop hat intensity profile along the horizontal axis.

In embodiments, light beam generators of interest may be configured toproduce angularly deflected laser beams in the output laser beam thatare spatially separated. Depending on the applied radiofrequency drivesignals and desired irradiation profile of the output laser beam, theangularly deflected laser beams may be separated by 0.001 μm or more,such as by 0.005 μm or more, such as by 0.01 μm or more, such as by 0.05μm or more, such as by 0.1 μm or more, such as by 0.5 μm or more, suchas by 1 μm or more, such as by 5 μm or more, such as by 10 μm or more,such as by 100 μm or more, such as by 500 μm or more, such as by 1000 μmor more and including by 5000 μm or more. In some embodiments, systemsare configured to produce angularly deflected laser beams in the outputlaser beam that overlap, such as with an adjacent angularly deflectedlaser beam along a horizontal axis of the output laser beam. The overlapbetween adjacent angularly deflected laser beams (such as overlap ofbeam spots) may be an overlap of 0.001 μm or more, such as an overlap of0.005 μm or more, such as an overlap of 0.01 μm or more, such as anoverlap of 0.05 μm or more, such as an overlap of 0.1 μm or more, suchas an overlap of 0.5 μm or more, such as an overlap of 1 μm or more,such as an overlap of 5 μm or more, such as an overlap of 10 μm or moreand including an overlap of 100 μm or more.

In certain instances, light beam generators configured to generate twoor more beams of frequency shifted light include laser excitationmodules as described in U.S. Pat. Nos. 9,423,353; 9,784,661 and10,006,852 and U.S. Patent Publication Nos. 2017/0133857 and2017/0350803, the disclosures of which are herein incorporated byreference. In embodiments, systems include a light detection systemhaving a plurality of photodetectors. Photodetectors of interest mayinclude, but are not limited to optical sensors, such as active-pixelsensors (APSs), avalanche photodiode, image sensors, charge-coupleddevices (CCDs), intensified charge-coupled devices (ICCDs), lightemitting diodes, photon counters, bolometers, pyroelectric detectors,photoresistors, photovoltaic cells, photodiodes, photomultiplier tubes,phototransistors, quantum dot photoconductors or photodiodes andcombinations thereof, among other photodetectors. In certainembodiments, light from a sample is measured with a charge-coupleddevice (CCD), semiconductor charge-coupled devices (CCD), active pixelsensors (APS), complementary metal-oxide semiconductor (CMOS) imagesensors or N-type metal-oxide semiconductor (NMOS) image sensors.

In some embodiments, light detection systems of interest include aplurality of photodetectors. In some instances, the light detectionsystem includes a plurality of solid-state detectors such asphotodiodes. In certain instances, the light detection system includes aphotodetector array, such as an array of photodiodes. In theseembodiments, the photodetector array may include 4 or morephotodetectors, such as 10 or more photodetectors, such as 25 or morephotodetectors, such as 50 or more photodetectors, such as 100 or morephotodetectors, such as 250 or more photodetectors, such as 500 or morephotodetectors, such as 750 or more photodetectors and including 1000 ormore photodetectors. For example, the detector may be a photodiode arrayhaving 4 or more photodiodes, such as 10 or more photodiodes, such as 25or more photodiodes, such as 50 or more photodiodes, such as 100 or morephotodiodes, such as 250 or more photodiodes, such as 500 or morephotodiodes, such as 750 or more photodiodes and including 1000 or morephotodiodes.

The photodetectors may be arranged in any geometric configuration asdesired, where arrangements of interest include, but are not limited toa square configuration, rectangular configuration, trapezoidalconfiguration, triangular configuration, hexagonal configuration,heptagonal configuration, octagonal configuration, nonagonalconfiguration, decagonal configuration, dodecagonal configuration,circular configuration, oval configuration as well as irregularpatterned configurations. The photodetectors in the photodetector arraymay be oriented with respect to the other (as referenced in an X-Zplane) at an angle ranging from 10° to 180°, such as from 15° to 170°,such as from 20° to 160°, such as from 25° to 150°, such as from 30° to120° and including from 45° to 90°. The photodetector array may be anysuitable shape and may be a rectilinear shape, e.g., squares,rectangles, trapezoids, triangles, hexagons, etc., curvilinear shapes,e.g., circles, ovals, as well as irregular shapes, e.g., a parabolicbottom portion coupled to a planar top portion. In certain embodiments,the photodetector array has a rectangular-shaped active surface.

Each photodetector (e.g., photodiode) in the array may have an activesurface with a width that ranges from 5 μm to 250 μm, such as from 10 μmto 225 μm, such as from 15 μm to 200 μm, such as from 20 μm to 175 μm,such as from 25 μm to 150 μm, such as from 30 μm to 125 μm and includingfrom 50 μm to 100 μm and a length that ranges from 5 μm to 250 μm, suchas from 10 μm to 225 μm, such as from 15 μm to 200 μm, such as from 20μm to 175 μm, such as from 25 μm to 150 μm, such as from 30 μm to 125 μmand including from 50 μm to 100 μm, where the surface area of eachphotodetector (e.g., photodiode) in the array ranges from 25 to μm² to10000 μm², such as from 50 to μm² to 9000 μm², such as from 75 to μm² to8000 μm², such as from 100 to μm² to 7000 μm², such as from 150 to μm²to 6000 μm² and including from 200 to μm² to 5000 μm².

The size of the photodetector array may vary depending on the amount andintensity of the light, the number of photodetectors and the desiredsensitivity and may have a length that ranges from 0.01 mm to 100 mm,such as from 0.05 mm to 90 mm, such as from 0.1 mm to 80 mm, such asfrom 0.5 mm to 70 mm, such as from 1 mm to 60 mm, such as from 2 mm to50 mm, such as from 3 mm to 40 mm, such as from 4 mm to 30 mm andincluding from 5 mm to 25 mm. The width of the photodetector array mayalso vary, ranging from 0.01 mm to 100 mm, such as from 0.05 mm to 90mm, such as from 0.1 mm to 80 mm, such as from 0.5 mm to 70 mm, such asfrom 1 mm to 60 mm, such as from 2 mm to 50 mm, such as from 3 mm to 40mm, such as from 4 mm to 30 mm and including from 5 mm to 25 mm. Assuch, the active surface of the photodetector array may range from 0.1mm² to 10000 mm², such as from 0.5 mm² to 5000 mm², such as from 1 mm²to 1000 mm², such as from 5 mm² to 500 mm², and including from 10 mm² to100 mm².

Photodetectors of interest are configured to measure collected light atone or more wavelengths, such as at 2 or more wavelengths, such as at 5or more different wavelengths, such as at 10 or more differentwavelengths, such as at 25 or more different wavelengths, such as at 50or more different wavelengths, such as at 100 or more differentwavelengths, such as at 200 or more different wavelengths, such as at300 or more different wavelengths and including measuring light emittedby a sample in the flow stream at 400 or more different wavelengths.

In some embodiments, photodetectors are configured to measure collectedlight over a range of wavelengths (e.g., 200 nm-1000 nm). In certainembodiments, photodetectors of interest are configured to collectspectra of light over a range of wavelengths. For example, systems mayinclude one or more detectors configured to collect spectra of lightover one or more of the wavelength ranges of 200 nm-1000 nm. In yetother embodiments, detectors of interest are configured to measure lightfrom the sample in the flow stream at one or more specific wavelengths.For example, systems may include one or more detectors configured tomeasure light at one or more of 450 nm, 518 nm, 519 nm, 561 nm, 578 nm,605 nm, 607 nm, 625 nm, 650 nm, 660 nm, 667 nm, 670 nm, 668 nm, 695 nm,710 nm, 723 nm, 780 nm, 785 nm, 647 nm, 617 nm and any combinationsthereof. In certain embodiments, photodetectors may be configured to bepaired with specific fluorophores, such as those used with the sample ina fluorescence assay. In some embodiments, photodetectors are configuredto measure collected light across the entire fluorescence spectrum ofeach fluorophore in the sample.

The light detection system is configured to measure light continuouslyor in discrete intervals. In some instances, photodetectors of interestare configured to take measurements of the collected light continuously.In other instances, the light detection system is configured to takemeasurements in discrete intervals, such as measuring light every 0.001millisecond, every 0.01 millisecond, every 0.1 millisecond, every 1millisecond, every 10 milliseconds, every 100 milliseconds and includingevery 1000 milliseconds, or some other interval.

In embodiments, systems are configured to analyze light from theirradiated sample and spectrally resolve light from each fluorophore inthe sample. In some embodiments, systems include memory havinginstructions stored thereon for determining the overlap between eachdifferent fluorophore in the sample and calculating the contribution ofeach fluorophore to the overlapping fluorescence. In certainembodiments, systems are configured to calculate a spectral unmixingmatrix for the fluorescence spectra of the plurality of fluorophoreshaving overlapping fluorescence in the sample detected by the lightdetection system. As described in greater detail below, systems may alsobe configured to estimate the abundance of each fluorophore in thesample. In certain embodiments, the abundance of each fluorophoreassociated with a target particle may be determined. The system may beconfigured to identify and classify a target particle based on theabundance of each fluorophore associated with the target particle may.In some instances, systems are configured to sort the identified orclassified particles. In these embodiments, systems may include computercontrolled systems where the systems further include one or morecomputers for complete automation or partial automation of a system forpracticing methods described herein. In some embodiments, systemsinclude a computer having a computer readable storage medium with acomputer program stored thereon, where the computer program when loadedon the computer includes instructions for irradiating a flow cell havinga sample in a flow stream with a light source and detecting light fromthe flow cell with a light detection system having a plurality ofphotodetectors, calculating a spectral unmixing matrix for thefluorescence spectra of the plurality of fluorophores for each particledetected by the light detection system, estimating the abundance of eachfluorophore using the spectral unmixing matrix; and sorting particles inthe sample based on the estimated fluorophore abundance.

In some embodiments, systems include a computer having a computerreadable storage medium with a computer program stored thereon, wherethe computer program when loaded on the computer further includesinstructions for spectrally resolving light from each fluorophore havingoverlapping fluorescence by calculating the spectral unmixing matrixusing a weighted least squares algorithm. In some instances, theweighted least squares algorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

where y is measured detector values from the plurality of photodetectorsof the light detection system for each cell; â is estimated fluorophoreabundance X is spillover; and W is

$\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}.$

In some embodiments, each W_(ii) is calculated according to:

$W_{ii} = {\frac{1}{\sigma_{t}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

where σ_(i) ² is variance at detector i; y_(i) is signal at detector i;and λ_(i) is constant noise at detector i. In certain embodiments, thespectral unmixing matrix is calculated according to: (X^(T)WX)⁻¹X^(T)W.In some instances, the subject systems include memory with instructionto invert (X^(T)WX) for each cell detected by the light detection systemto calculate a spectral unmixing matrix. In certain embodiments, systemsinclude a computer having a computer readable storage medium with acomputer program stored thereon, where the computer program when loadedon the computer further includes instructions for approximating theinversion of (X^(T)WX) in the weighted least square algorithm for eachcell detected by the light detection system in order to sort cells inthe sample in real time. In some embodiments, the computer program whenloaded on the computer further includes instructions for inverting(X^(T)WX) includes approximating (X^(T)WX) using an iterativeNewton-Raphson calculation according to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

where W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system.

In some embodiments, systems include a computer having a computerreadable storage medium with a computer program stored thereon, wherethe computer program when loaded on the computer further includesinstructions for estimating the variance of each photodetector. In someinstances, the instructions include determining the photodetector noisecomponents (e.g., electronic noise, background light, etc.) using asingle stain control sample. In other instances, the instructionsinclude determining the variance of each photodetector beforeirradiating the sample with the light source. In yet other instances,the instructions include determining the predetermined approximation ofW, W_(G), before irradiating the sample with the light source. Incertain embodiments, the memory includes instructions stored thereon,which when executed by the processor, cause the processor to precomputeA₀ ⁻¹ with the predetermined W_(G). In these embodiments, theprecomputed A₀ ⁻¹ may be stored in the memory and used by the processoras a first approximation of the A⁻¹ for each particle detected by thelight detection system.

In other embodiments, systems include a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor toapproximate the weighted least square algorithm for each particle with aSherman-Morrison iterative inverse updater. In some instances, thememory includes instructions for computing A using the Sherman-Morrisonformula:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - \frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}}$

In certain instances, the memory includes instructions for precomputingA₀ ⁻¹ to compute the inverse of a perturbation of A₀ using theSherman-Morrison formula. In some embodiments, the inverse of A₀ iscalculated by the formula X^(T)W₀X and the inverse of A is calculated bythe formula X^(T)WX. In some instances, the memory includes instructionsfor calculating ΔA (i.e., A−A₀) as a product of column vectors with eachiterative W according to:

$W_{0} = {{\begin{bmatrix}w_{11}^{0} & 0 & \ldots & 0 \\0 & w_{22}^{0} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}^{0}\end{bmatrix}\mspace{14mu}{and}\mspace{14mu} W} = \begin{bmatrix}w_{11} & 0 & \ldots & 0 \\0 & w_{22} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}\end{bmatrix}}$

-   -   where w_(ii)=w⁰ _(ii)+α_(i) for iϵ[1, N_(D)].

${W_{1} = {W_{0} + \begin{bmatrix}\alpha_{1} & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}},{W_{2} = {{W_{1} + \begin{bmatrix}0 & 0 & \ldots & 0 \\0 & \alpha_{2} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}❘\mspace{14mu}{and}}}$${W = {W_{N_{D}} = {W_{N_{D} - 1} + {\begin{bmatrix}0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \alpha_{N_{D}}\end{bmatrix}\mspace{14mu}{and}}}}}\mspace{11mu}$${\Delta\; W_{i}} = {{W_{i} - W} = \begin{bmatrix}0 & 0 & 0 & \ldots & 0 \\\vdots & \ddots & \vdots & \vdots & 0 \\0 & \ldots & \alpha_{i} & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & \ldots & 0\end{bmatrix}}$

According to embodiments, ΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) whereA can be expressed as:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

In these embodiments, each A can be recomputed from A₀ with each newweight matrix W (i.e., with different values from W₀) using the changeto each w_(i). In some embodiments, systems include a processor withmemory operably coupled to the processor where the memory includesinstructions stored thereon, which when executed by the processor, causethe processor to perform a Sherman-Morrison iterative inverse updaterfor approximating the spectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

In some embodiments, a precomputed value for A₀ ⁻¹ is used to calculateA₁ ⁻¹. The precomputed A₁ ⁻¹ is then used to calculate A₂ ⁻¹. The valueA⁻¹ can be calculated by repeat computing of A_(i) ⁻¹ using each(A_(i−1))⁻¹ from i=1 to N_(D). In certain embodiments, the subjectsystems include a field programmable gate array and the spectralunmixing algorithm is calculated for each cell in real time on a fieldprogrammable gated array.

In other embodiments, systems include a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor tocalculate the weighted least square algorithm for each particle bymatrix decomposition. In some instances, the memory includesinstructions for a LU matrix decomposition, such as where a matrix isdecomposed into a product of a lower-triangular (L) matrix and anupper-triangular (U) matrix. In certain instances, LU decompositionincludes Gaussian elimination. In other instances, LU decompositionincludes a modified Cholesky decomposition, an LDL decomposition where Dis diagonal matrix. In certain embodiments, systems include a processorwith memory operably coupled to the processor where the memory includesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm (a)using a modified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B LDL decomposition

Lz=B where z=DL ^(T) a Lower-triangular matrix solution

Dx=z where x=L ^(T) a Diagonal matrix solution

L ^(T) a=x Upper-triangular matrix solution

In other embodiments, systems include a processor with memory operablycoupled to the processor where the memory includes instructions storedthereon, which when executed by the processor, cause the processor tocalculate a weighted least squares algorithm by QR factorization. Insome instances, the QR factorization is a matrix that is the product ofan orthogonal (Q) matrix and an upper-triangular (R) matrix. In someembodiments, the memory includes instructions for calculating theweighted least squares algorithm (a) using QR factorization accordingto:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X (QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

In yet other embodiments, systems include a processor with memoryoperably coupled to the processor where the memory includes instructionsstored thereon, which when executed by the processor, cause theprocessor to calculate a weighted least squares algorithm by singularvalue decomposition (SVD). In some instances, the singular valuedecomposition is the matrix that is the product X=UΣV^(T) where U and Vare orthogonal matrices and Z is a diagonal matrix containing singularvalues of X. In certain instances, the memory includes instructions forcalculating the weighted least squares algorithm (a) using singularvalue decomposition according to:

z=U ^(T) y

Σw=z

a=Vw

In some embodiments, systems include a computer having a computerreadable storage medium with a computer program stored thereon, wherethe computer program when loaded on the computer further includesinstructions for calculating the abundance of one or more fluorophoresin the sample from the spectrally resolved light from each fluorophore.In certain instances, the abundance of fluorophores associated with(e.g., chemically associated (i.e., covalently, ionically) or physicallyassociated) a target particle is calculated from the spectrally resolvedlight from each fluorophore associated with the particle. For instance,in one example the relative abundance of each fluorophore associatedwith a target particle is calculated from the spectrally resolved lightfrom each fluorophore. In another example, the absolute abundance ofeach fluorophore associated with the target particle is calculated fromthe spectrally resolved light from each fluorophore.

In certain embodiments, systems are configured to identify or classify aparticle based on the relative abundance of each fluorophore determinedto be associated with the particle. In these embodiments, the subjectsystems may be configured to identify or classify the particle by anyconvenient protocol such as by: comparing the relative or absoluteabundance of each fluorophore associated with a particle with a controlsample having particles of known identity; or by conductingspectroscopic or other assay analysis of a population of particles(e.g., cells) having the calculated relative or absolute abundance ofassociated fluorophores.

Systems according to some embodiments, may include a display andoperator input device. Operator input devices may, for example, be akeyboard, mouse, or the like. The processing module includes a processorwhich has access to a memory having instructions stored thereon forperforming the steps of the subject methods. The processing module mayinclude an operating system, a graphical user interface (GUI)controller, a system memory, memory storage devices, and input-outputcontrollers, cache memory, a data backup unit, and many other devices.The processor may be a commercially available processor or it may be oneof other processors that are or will become available. The processorexecutes the operating system and the operating system interfaces withfirmware and hardware in a well-known manner, and facilitates theprocessor in coordinating and executing the functions of variouscomputer programs that may be written in a variety of programminglanguages, such as Java, Perl, C++, other high level or low-levellanguages, as well as combinations thereof, as is known in the art. Theoperating system, typically in cooperation with the processor,coordinates and executes functions of the other components of thecomputer. The operating system also provides scheduling, input-outputcontrol, file and data management, memory management, and communicationcontrol and related services, all in accordance with known techniques.The processor may be any suitable analog or digital system. In someembodiments, the processor includes analog electronics which providefeedback control, such as for example negative feedback control.

The system memory may be any of a variety of known or future memorystorage devices. Examples include any commonly available random-accessmemory (RAM), magnetic medium such as a resident hard disk or tape, anoptical medium such as a read and write compact disc, flash memorydevices, or other memory storage device. The memory storage device maybe any of a variety of known or future devices, including a compact diskdrive, a tape drive, a removable hard disk drive, or a diskette drive.Such types of memory storage devices typically read from, and/or writeto, a program storage medium (not shown) such as, respectively, acompact disk, magnetic tape, removable hard disk, or floppy diskette.Any of these program storage media, or others now in use or that maylater be developed, may be considered a computer program product. Aswill be appreciated, these program storage media typically store acomputer software program and/or data. Computer software programs, alsocalled computer control logic, typically are stored in system memoryand/or the program storage device used in conjunction with the memorystorage device.

In some embodiments, a computer program product is described comprisinga computer usable medium having control logic (computer softwareprogram, including program code) stored therein. The control logic, whenexecuted by the processor the computer, causes the processor to performfunctions described herein. In other embodiments, some functions areimplemented primarily in hardware using, for example, a hardware statemachine. Implementation of the hardware state machine so as to performthe functions described herein will be apparent to those skilled in therelevant arts.

Memory may be any suitable device in which the processor can store andretrieve data, such as magnetic, optical, or solid-state storage devices(including magnetic or optical disks or tape or RAM, or any othersuitable device, either fixed or portable). The processor may include ageneral-purpose digital microprocessor suitably programmed from acomputer readable medium carrying necessary program code. Programmingcan be provided remotely to processor through a communication channel,or previously saved in a computer program product such as memory or someother portable or fixed computer readable storage medium using any ofthose devices in connection with memory. For example, a magnetic oroptical disk may carry the programming, and can be read by a diskwriter/reader. Systems of the invention also include programming, e.g.,in the form of computer program products, algorithms for use inpracticing the methods as described above. Programming according to thepresent invention can be recorded on computer readable media, e.g., anymedium that can be read and accessed directly by a computer. Such mediainclude, but are not limited to: magnetic storage media, such as floppydiscs, hard disc storage medium, and magnetic tape; optical storagemedia such as CD-ROM; electrical storage media such as RAM and ROM;portable flash drive; and hybrids of these categories such asmagnetic/optical storage media.

The processor may also have access to a communication channel tocommunicate with a user at a remote location. By remote location ismeant the user is not directly in contact with the system and relaysinput information to an input manager from an external device, such as acomputer connected to a Wide Area Network (“WAN”), telephone network,satellite network, or any other suitable communication channel,including a mobile telephone (i.e., smartphone).

In some embodiments, systems according to the present disclosure may beconfigured to include a communication interface. In some embodiments,the communication interface includes a receiver and/or transmitter forcommunicating with a network and/or another device. The communicationinterface can be configured for wired or wireless communication,including, but not limited to, radio frequency (RF) communication (e.g.,Radio-Frequency Identification (RFID), Zigbee communication protocols,WiFi, infrared, wireless Universal Serial Bus (USB), Ultra-Wide Band(UWB), Bluetooth® communication protocols, and cellular communication,such as code division multiple access (CDMA) or Global System for Mobilecommunications (GSM).

In one embodiment, the communication interface is configured to includeone or more communication ports, e.g., physical ports or interfaces suchas a USB port, an RS-232 port, or any other suitable electricalconnection port to allow data communication between the subject systemsand other external devices such as a computer terminal (for example, ata physician's office or in hospital environment) that is configured forsimilar complementary data communication.

In one embodiment, the communication interface is configured forinfrared communication, Bluetooth® communication, or any other suitablewireless communication protocol to enable the subject systems tocommunicate with other devices such as computer terminals and/ornetworks, communication enabled mobile telephones, personal digitalassistants, or any other communication devices which the user may use inconjunction.

In one embodiment, the communication interface is configured to providea connection for data transfer utilizing Internet Protocol (IP) througha cell phone network, Short Message Service (SMS), wireless connectionto a personal computer (PC) on a Local Area Network (LAN) which isconnected to the internet, or WiFi connection to the internet at a WiFihotspot.

In one embodiment, the subject systems are configured to wirelesslycommunicate with a server device via the communication interface, e.g.,using a common standard such as 802.11 or Bluetooth® RF protocol, or anIrDA infrared protocol. The server device may be another portabledevice, such as a smart phone, Personal Digital Assistant (PDA) ornotebook computer; or a larger device such as a desktop computer,appliance, etc. In some embodiments, the server device has a display,such as a liquid crystal display (LCD), as well as an input device, suchas buttons, a keyboard, mouse or touch-screen.

In some embodiments, the communication interface is configured toautomatically or semi-automatically communicate data stored in thesubject systems, e.g., in an optional data storage unit, with a networkor server device using one or more of the communication protocols and/ormechanisms described above.

Output controllers may include controllers for any of a variety of knowndisplay devices for presenting information to a user, whether a human ora machine, whether local or remote. If one of the display devicesprovides visual information, this information typically may be logicallyand/or physically organized as an array of picture elements. A graphicaluser interface (GUI) controller may include any of a variety of known orfuture software programs for providing graphical input and outputinterfaces between the system and a user, and for processing userinputs. The functional elements of the computer may communicate witheach other via system bus. Some of these communications may beaccomplished in alternative embodiments using network or other types ofremote communications. The output manager may also provide informationgenerated by the processing module to a user at a remote location, e.g.,over the Internet, phone or satellite network, in accordance with knowntechniques. The presentation of data by the output manager may beimplemented in accordance with a variety of known techniques. As someexamples, data may include SQL, HTML or XML documents, email or otherfiles, or data in other forms. The data may include Internet URLaddresses so that a user may retrieve additional SQL, HTML, XML, orother documents or data from remote sources. The one or more platformspresent in the subject systems may be any type of known computerplatform or a type to be developed in the future, although theytypically will be of a class of computer commonly referred to asservers. However, they may also be a main-frame computer, a workstation, or other computer type. They may be connected via any known orfuture type of cabling or other communication system including wirelesssystems, either networked or otherwise. They may be co-located or theymay be physically separated. Various operating systems may be employedon any of the computer platforms, possibly depending on the type and/ormake of computer platform chosen. Appropriate operating systems includeWindows 10, Windows NT®, Windows XP, Windows 7, Windows 8, iOS, SunSolaris, Linux, OS/400, Compaq Tru64 Unix, SGI IRIX, Siemens ReliantUnix, Ubuntu, Zorin OS and others.

In certain embodiments, the subject systems include one or more opticaladjustment components for adjusting the light such as light irradiatedonto the sample (e.g., from a laser) or light collected from the sample(e.g., scattered, fluorescence). For example, the optical adjustment maybe to increase the dimensions of the light, the focus of the light or tocollimate the light. In some instances, optical adjustment is amagnification protocol so as to increase the dimensions of the light(e.g., beam spot), such as increasing the dimensions by 5% or more, suchas by 10% or more, such as by 25% or more, such as by 50% or more andincluding increasing the dimensions by 75% or more. In otherembodiments, optical adjustment includes focusing the light so as toreduce the light dimensions, such as by 5% or greater, such as by 10% orgreater, such as by 25% or greater, such as by 50% or greater andincluding reducing the dimensions of the beam spot by 75% or greater. Incertain embodiments, optical adjustment includes collimating the light.The term “collimate” is used in its conventional sense to refer to theoptically adjusting the collinearity of light propagation or reducingdivergence by the light of from a common axis of propagation. In someinstances, collimating includes narrowing the spatial cross section of alight beam (e.g., reducing the beam profile of a laser)

In some embodiments, the optical adjustment component is a focusing lenshaving a magnification ratio of from 0.1 to 0.95, such as amagnification ratio of from 0.2 to 0.9, such as a magnification ratio offrom 0.3 to 0.85, such as a magnification ratio of from 0.35 to 0.8,such as a magnification ratio of from 0.5 to 0.75 and including amagnification ratio of from 0.55 to 0.7, for example a magnificationratio of 0.6. For example, the focusing lens is, in certain instances, adouble achromatic de-magnifying lens having a magnification ratio ofabout 0.6. The focal length of the focusing lens may vary, ranging from5 mm to 20 mm, such as from 6 mm to 19 mm, such as from 7 mm to 18 mm,such as from 8 mm to 17 mm, such as from 9 mm to 16 and including afocal length ranging from 10 mm to 15 mm. In certain embodiments, thefocusing lens has a focal length of about 13 mm.

In other embodiments, the optical adjustment component is a collimator.The collimator may be any convenient collimating protocol, such as oneor more mirrors or curved lenses or a combination thereof. For example,the collimator is in certain instances a single collimating lens. Inother instances, the collimator is a collimating mirror. In yet otherinstances, the collimator includes two lenses. In still other instances,the collimator includes a mirror and a lens. Where the collimatorincludes one or more lenses, the focal length of the collimating lensmay vary, ranging from 5 mm to 40 mm, such as from 6 mm to 37.5 mm, suchas from 7 mm to 35 mm, such as from 8 mm to 32.5 mm, such as from 9 mmto 30 mm, such as from 10 mm to 27.5 mm, such as from 12.5 mm to 25 mmand including a focal length ranging from 15 mm to 20 mm.

In some embodiments, the subject systems include a flow cell nozzlehaving a nozzle orifice configured to flow a flow stream through theflow cell nozzle. The subject flow cell nozzle has an orifice whichpropagates a fluidic sample to a sample interrogation region, where insome embodiments, the flow cell nozzle includes a proximal cylindricalportion defining a longitudinal axis and a distal frustoconical portionwhich terminates in a flat surface having the nozzle orifice that istransverse to the longitudinal axis. The length of the proximalcylindrical portion (as measured along the longitudinal axis) may varyranging from 1 mm to 15 mm, such as from 1.5 mm to 12.5 mm, such as from2 mm to 10 mm, such as from 3 mm to 9 mm and including from 4 mm to 8mm. The length of the distal frustoconical portion (as measured alongthe longitudinal axis) may also vary, ranging from 1 mm to 10 mm, suchas from 2 mm to 9 mm, such as from 3 mm to 8 mm and including from 4 mmto 7 mm. The diameter of the of the flow cell nozzle chamber may vary,in some embodiments, ranging from 1 mm to 10 mm, such as from 2 mm to 9mm, such as from 3 mm to 8 mm and including from 4 mm to 7 mm.

In certain instances, the nozzle chamber does not include a cylindricalportion and the entire flow cell nozzle chamber is frustoconicallyshaped. In these embodiments, the length of the frustoconical nozzlechamber (as measured along the longitudinal axis transverse to thenozzle orifice), may range from 1 mm to 15 mm, such as from 1.5 mm to12.5 mm, such as from 2 mm to 10 mm, such as from 3 mm to 9 mm andincluding from 4 mm to 8 mm. The diameter of the proximal portion of thefrustoconical nozzle chamber may range from 1 mm to 10 mm, such as from2 mm to 9 mm, such as from 3 mm to 8 mm and including from 4 mm to 7 mm.

In embodiments, the sample flow stream emanates from an orifice at thedistal end of the flow cell nozzle. Depending on the desiredcharacteristics of the flow stream, the flow cell nozzle orifice may beany suitable shape where cross-sectional shapes of interest include, butare not limited to: rectilinear cross sectional shapes, e.g., squares,rectangles, trapezoids, triangles, hexagons, etc., curvilinearcross-sectional shapes, e.g., circles, ovals, as well as irregularshapes, e.g., a parabolic bottom portion coupled to a planar topportion. In certain embodiments, flow cell nozzle of interest has acircular orifice. The size of the nozzle orifice may vary, in someembodiments ranging from 1 μm to 20000 μm, such as from 2 μm to 17500μm, such as from 5 μm to 15000 μm, such as from 10 μm to 12500 μm, suchas from 15 μm to 10000 μm, such as from 25 μm to 7500 μm, such as from50 μm to 5000 μm, such as from 75 μm to 1000 μm, such as from 100 μm to750 μm and including from 150 μm to 500 μm. In certain embodiments, thenozzle orifice is 100 μm.

In some embodiments, the flow cell nozzle includes a sample injectionport configured to provide a sample to the flow cell nozzle. Inembodiments, the sample injection system is configured to providesuitable flow of sample to the flow cell nozzle chamber. Depending onthe desired characteristics of the flow stream, the rate of sampleconveyed to the flow cell nozzle chamber by the sample injection portmay be 1 μL/sec or more, such as 2 μL/sec or more, such as 3 μL/sec ormore, such as 5 μL/sec or more, such as 10 μL/sec or more, such as 15μL/sec or more, such as 25 μL/sec or more, such as 50 μL/sec or more,such as 100 μL/sec or more, such as 150 μL/sec or more, such as 200μL/sec or more, such as 250 μL/sec or more, such as 300 μt/sec or more,such as 350 μL/sec or more, such as 400 μL/sec or more, such as 450μL/sec or more and including 500 μL/sec or more. For example, the sampleflow rate may range from 1 μL/sec to about 500 μL/sec, such as from 2μL/sec to about 450 μL/sec, such as from 3 μL/sec to about 400 μL/sec,such as from 4 μL/sec to about 350 μL/sec, such as from 5 μL/sec toabout 300 μL/sec, such as from σμL/sec to about 250 μL/sec, such as from7 μL/sec to about 200 μL/sec, such as from 8 μL/sec to about 150 μL/sec,such as from 9 μL/sec to about 125 μL/sec and including from 10 μL/secto about 100 μL/sec.

The sample injection port may be an orifice positioned in a wall of thenozzle chamber or may be a conduit positioned at the proximal end of thenozzle chamber. Where the sample injection port is an orifice positionedin a wall of the nozzle chamber, the sample injection port orifice maybe any suitable shape where cross-sectional shapes of interest include,but are not limited to: rectilinear cross sectional shapes, e.g.,squares, rectangles, trapezoids, triangles, hexagons, etc., curvilinearcross-sectional shapes, e.g., circles, ovals, etc., as well as irregularshapes, e.g., a parabolic bottom portion coupled to a planar topportion. In certain embodiments, the sample injection port has acircular orifice. The size of the sample injection port orifice may varydepending on shape, in certain instances, having an opening ranging from0.1 mm to 5.0 mm, e.g., 0.2 to 3.0 mm, e.g., 0.5 mm to 2.5 mm, such asfrom 0.75 mm to 2.25 mm, such as from 1 mm to 2 mm and including from1.25 mm to 1.75 mm, for example 1.5 mm.

In certain instances, the sample injection port is a conduit positionedat a proximal end of the flow cell nozzle chamber. For example, thesample injection port may be a conduit positioned to have the orifice ofthe sample injection port in line with the flow cell nozzle orifice.Where the sample injection port is a conduit positioned in line with theflow cell nozzle orifice, the cross-sectional shape of the sampleinjection tube may be any suitable shape where cross-sectional shapes ofinterest include, but are not limited to: rectilinear cross sectionalshapes, e.g., squares, rectangles, trapezoids, triangles, hexagons,etc., curvilinear cross-sectional shapes, e.g., circles, ovals, as wellas irregular shapes, e.g., a parabolic bottom portion coupled to aplanar top portion. The orifice of the conduit may vary depending onshape, in certain instances, having an opening ranging from 0.1 mm to5.0 mm, e.g., 0.2 to 3.0 mm, e.g., 0.5 mm to 2.5 mm, such as from 0.75mm to 2.25 mm, such as from 1 mm to 2 mm and including from 1.25 mm to1.75 mm, for example 1.5 mm. The shape of the tip of the sampleinjection port may be the same or different from the cross-section shapeof the sample injection tube. For example, the orifice of the sampleinjection port may include a beveled tip having a bevel angle rangingfrom 1° to 10°, such as from 2° to 9°, such as from 3° to 8°, such asfrom 4° to 7° and including a bevel angle of 5°.

In some embodiments, the flow cell nozzle also includes a sheath fluidinjection port configured to provide a sheath fluid to the flow cellnozzle. In embodiments, the sheath fluid injection system is configuredto provide a flow of sheath fluid to the flow cell nozzle chamber, forexample in conjunction with the sample to produce a laminated flowstream of sheath fluid surrounding the sample flow stream. Depending onthe desired characteristics of the flow stream, the rate of sheath fluidconveyed to the flow cell nozzle chamber by the may be 254 μL/sec ormore, such as 50 μL/sec or more, such as 75 μL/sec or more, such as 100μL/sec or more, such as 250 μL/sec or more, such as 500 μL/sec or more,such as 750 μL/sec or more, such as 1000 μL/sec or more and including2500 μL/sec or more. For example, the sheath fluid flow rate may rangefrom 1 μL/sec to about 500 μL/sec, such as from 2 μL/sec to about 450μL/sec, such as from 3 μL/sec to about 400 μL/sec, such as from 4 μL/secto about 350 μL/sec, such as from 5 μL/sec to about 300 μL/sec, such asfrom 6 μL/sec to about 250 μL/sec, such as from 7 μL/sec to about 200μL/sec, such as from 8 μL/sec to about 150 μL/sec, such as from 9 μL/secto about 125 μL/sec and including from 10 μL/sec to about 100 μL/sec.

In some embodiments, the sheath fluid injection port is an orificepositioned in a wall of the nozzle chamber. The sheath fluid injectionport orifice may be any suitable shape where cross-sectional shapes ofinterest include, but are not limited to: rectilinear cross sectionalshapes, e.g., squares, rectangles, trapezoids, triangles, hexagons,etc., curvilinear cross-sectional shapes, e.g., circles, ovals, as wellas irregular shapes, e.g., a parabolic bottom portion coupled to aplanar top portion. The size of the sample injection port orifice mayvary depending on shape, in certain instances, having an opening rangingfrom 0.1 mm to 5.0 mm, e.g., 0.2 to 3.0 mm, e.g., 0.5 mm to 2.5 mm, suchas from 0.75 mm to 2.25 mm, such as from 1 mm to 2 mm and including from1.25 mm to 1.75 mm, for example 1.5 mm.

The subject systems, in certain instances, include a sampleinterrogation region in fluid communication with the flow cell nozzleorifice. In these instances, a sample flow stream emanates from anorifice at the distal end of the flow cell nozzle and particles in theflow stream may be irradiated with a light source at the sampleinterrogation region. The size of the interrogation region may varydepending on the properties of the flow nozzle, such as the size of thenozzle orifice and sample injection port size. In embodiments, theinterrogation region may have a width that is 0.01 mm or more, such as0.05 mm or more, such as 0.1 mm or more, such as 0.5 mm or more, such as1 mm or more, such as 2 mm or more, such as 3 mm or more, such as 5 mmor more and including 10 mm or more. The length of the interrogationregion may also vary, ranging in some instances along 0.01 mm or more,such as 0.1 mm or more, such as 0.5 mm or more, such as 1 mm or more,such as 1.5 mm or more, such as 2 mm or more, such as 3 mm or more, suchas 5 mm or more, such as 10 or more, such as 15 mm or more, such as 20mm or more, such as 25 mm or more and including 50 mm or more.

The interrogation region may be configured to facilitate irradiation ofa planar cross-section of an emanating flow stream or may be configuredto facilitate irradiation of a diffuse field (e.g., with a diffuse laseror lamp) of a predetermined length. In some embodiments, theinterrogation region includes a transparent window that facilitatesirradiation of a predetermined length of an emanating flow stream, suchas 1 mm or more, such as 2 mm or more, such as 3 mm or more, such as 4mm or more, such as 5 mm or more and including 10 mm or more. Dependingon the light source used to irradiate the emanating flow stream (asdescribed below), the interrogation region may be configured to passlight that ranges from 100 nm to 1500 nm, such as from 150 nm to 1400nm, such as from 200 nm to 1300 nm, such as from 250 nm to 1200 nm, suchas from 300 nm to 1100 nm, such as from 350 nm to 1000 nm, such as from400 nm to 900 nm and including from 500 nm to 800 nm. As such, theinterrogation region may be formed from any transparent material whichpasses the desired range of wavelength, including but not limited tooptical glass, borosilicate glass, Pyrex glass, ultraviolet quartz,infrared quartz, sapphire as well as plastic, such as polycarbonates,polyvinyl chloride (PVC), polyurethanes, polyethers, polyamides,polyimides, or copolymers of these thermoplastics, such as PETG(glycol-modified polyethylene terephthalate), among other polymericplastic materials, including polyester, where polyesters of interest mayinclude, but are not limited to poly(alkylene terephthalates) such aspoly(ethylene terephthalate) (PET), bottle-grade PET (a copolymer madebased on monoethylene glycol, terephthalic acid, and other comonomerssuch as isophthalic acid, cyclohexene dimethanol, etc.), poly(butyleneterephthalate) (PBT), and poly(hexamethylene terephthalate);poly(alkylene adipates) such as poly(ethylene adipate),poly(1,4-butylene adipate), and poly(hexamethylene adipate);poly(alkylene suberates) such as poly(ethylene suberate); poly(alkylenesebacates) such as poly(ethylene sebacate); poly(ϵ-caprolactone) andpoly(β-propiolactone); poly(alkylene isophthalates) such aspoly(ethylene isophthalate); poly(alkylene2,6-naphthalene-dicarboxylates) such as poly(ethylene2,6-naphthalene-dicarboxylate); poly(alkylene sulfonyl-4,4′-dibenzoates)such as poly(ethylene sulfonyl-4,4′-dibenzoate); poly(p-phenylenealkylene dicarboxylates) such as poly(p-phenylene ethylenedicarboxylates); poly(trans-1,4-cyclohexanediyl alkylene dicarboxylates)such as poly(trans-1,4-cyclohexanediyl ethylene dicarboxylate);poly(1,4-cyclohexane-dimethylene alkylene dicarboxylates) such aspoly(1,4-cyclohexane-dimethylene ethylene dicarboxylate);poly([2.2.2]-bicyclooctane-1,4-dimethylene alkylene dicarboxylates) suchas poly([2.2.2]-bicyclooctane-1,4-dimethylene ethylene dicarboxylate);lactic acid polymers and copolymers such as (S)-polylactide,(R,S)-polylactide, poly(tetramethylglycolide), andpoly(lactide-co-glycolide); and polycarbonates of bisphenol A,3,3′-dimethylbisphenol A, 3,3′,5,5′-tetrachlorobisphenol A,3,3′,5,5′-tetramethylbisphenol A; polyamides such as poly(p-phenyleneterephthalamide); polyesters, e.g., polyethylene terephthalates, e.g.,Mylar™ polyethylene terephthalate; etc. In some embodiments, the subjectsystems include a cuvette positioned in the sample interrogation region.In embodiments, the cuvette may pass light that ranges from 100 nm to1500 nm, such as from 150 nm to 1400 nm, such as from 200 nm to 1300 nm,such as from 250 nm to 1200 nm, such as from 300 nm to 1100 nm, such asfrom 350 nm to 1000 nm, such as from 400 nm to 900 nm and including from500 nm to 800 nm.

In certain embodiments, the subject systems are flow cytometric systemsemploying the above described weighted least squares algorithm foranalyzing and sorting particles in a sample (e.g., cells in a biologicalsample). Suitable flow cytometry systems may include, but are notlimited to those described in Ormerod (ed.), Flow Cytometry: A PracticalApproach, Oxford Univ. Press (1997); Jaroszeski et al. (eds.), FlowCytometry Protocols, Methods in Molecular Biology No. 91, Humana Press(1997); Practical Flow Cytometry, 3rd ed., Wiley-Liss (1995); Virgo, etal. (2012) Ann Clin Biochem. January; 49(pt 1):17-28; Linden, et. al.,Semin Throm Hemost. 2004 October; 30(5):502-11; Alison, et al. J Pathol,2010 December; 222(4):335-344; and Herbig, et al. (2007) Crit Rev TherDrug Carrier Syst. 24(3):203-255; the disclosures of which areincorporated herein by reference. In certain instances, flow cytometrysystems of interest include BD Biosciences FACSCanto™ II flow cytometer,BD Accuri™ flow cytometer, BD Biosciences FACSCelesta™ flow cytometer,BD Biosciences FACSLyric™ flow cytometer, BD Biosciences FACSVerse™ flowcytometer, BD Biosciences FACSymphony™ flow cytometer BD BiosciencesLSRFortessa™ flow cytometer, BD Biosciences LSRFortess™ X-20 flowcytometer and BD Biosciences FACSCalibur™ cell sorter, a BD BiosciencesFACSCount™ cell sorter, BD Biosciences FACSLyric™ cell sorter and BDBiosciences Via™ cell sorter BD Biosciences Influx™ cell sorter, BDBiosciences Jazz™ cell sorter, BD Biosciences Aria™ cell sorters and BDBiosciences FACSMelody™ cell sorter, or the like.

In some embodiments, the subject particle sorting systems are flowcytometric systems, such those described in U.S. Pat. Nos. 9,952,076;9,933,341; 9,726,527; 9,453,789; 9,200,334; 9,097,640; 9,095,494;9,092,034; 8,975,595; 8,753,573; 8,233,146; 8,140,300; 7,544,326;7,201,875; 7,129,505; 6,821,740; 6,813,017; 6,809,804; 6,372,506;5,700,692; 5,643,796; 5,627,040; 5,620,842; 5,602,039; the disclosure ofwhich are herein incorporated by reference in their entirety.

In certain embodiments, the subject systems are configured to sort oneor more of the particles (e.g., cells) of the sample that are identifiedbased on the estimated abundance of the fluorophores associated with theparticle as described above. The term “sorting” is used herein in itsconventional sense to refer to separating components (e.g., cells,non-cellular particles such as biological macromolecules) of the sampleand in some instances delivering the separated components to one or moresample collection containers. For example, the subject systems may beconfigured for sorting samples having 2 or more components, such as 3 ormore components, such as 4 or more components, such as 5 or morecomponents, such as 10 or more components, such as 15 or more componentsand including soring a sample having 25 or more components. One or moreof the sample components may be separated from the sample and deliveredto a sample collection container, such as 2 or more sample components,such as 3 or more sample components, such as 4 or more samplecomponents, such as 5 or more sample components, such as 10 or moresample components and including 15 or more sample components may beseparated from the sample and delivered to a sample collectioncontainer.

In some embodiments, particle sorting systems of interest are configuredto sort particles with an enclosed particle sorting module, such asthose described in U.S. Patent Publication No. 2017/0299493, filed onMar. 28, 2017, the disclosure of which is incorporated herein byreference. In certain embodiments, particles (e.g, cells) of the sampleare sorted using a sort decision module having a plurality of sortdecision units, such as those described in U.S. Provisional PatentApplication No. 62/803,264, filed on Feb. 8, 2019, the disclosure ofwhich is incorporated herein by reference. In some embodiments, methodsfor sorting components of sample include sorting particles (e.g., cellsin a biological sample) with a particle sorting module having deflectorplates, such as described in U.S. Patent Publication No. 2017/0299493,filed on Mar. 28, 2017, the disclosure of which is incorporated hereinby reference.

Integrated Circuit Devices

Aspects of the present disclosure also include integrated circuitdevices programmed to spectrally resolve light from each fluorophore inthe sample comprising a plurality of fluorophores having overlappingfluorescence spectra. In some embodiments, integrated circuit devices ofinterest include a field programmable gate array (FPGA). In otherembodiments, integrated circuit devices include an application specificintegrated circuit (ASIC). In yet other embodiments, integrated circuitdevices include a complex programmable logic device (CPLD). In someembodiments, the subject integrated circuit devices are programmed todetermine the overlap between each different fluorophore in the sampleand calculate the contribution of each fluorophore to the overlappingfluorescence. In certain embodiments, the integrated circuit isprogrammed to calculate a spectral unmixing matrix for fluorescencespectra of a plurality of fluorophores having overlapping fluorescencein a sample detected by a light detection system having a plurality ofphotodetectors. In certain embodiments, integrated circuit devicesaccording to certain embodiments are programmed to calculate a spectralunmixing matrix for fluorescence spectra of a plurality of fluorophoresfor each cell in a sample. As described in greater detail below,integrated circuit devices may be programmed to estimate the abundanceof each fluorophore in the sample. In certain embodiments, the abundanceof each fluorophore associated with a target particle may be determined.The integrated circuit may be programmed to identify and classify atarget particle based on the abundance of each fluorophore associatedwith the target particle may. In some instances, integrated circuits areconfigured to sort the identified or classified particles.

In some embodiments, the integrated circuit is programmed to calculatethe spectral unmixing matrix using a weighted least squares algorithm.In some instances, the integrated circuit is programmed to calculate theweighted least squares algorithm according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

where y is measured detector values from the plurality of photodetectorsof the light detection system for each cell; â is estimated fluorophoreabundance X is spillover; and W is

$\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}.$

In some embodiments, each W_(ii) is calculated according to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

where σ_(i) ² is variance at detector i; y_(i) is signal at detector i;and λ_(i) is constant noise at detector i. In certain embodiments, thefield programmable gate array is configured the calculate spectralunmixing matrix according to: (X^(T)WX)⁻¹X^(T)W. In some instances, themethod comprises inverting (X^(T)WX) for each cell detected by the lightdetection system to calculate a spectral unmixing matrix. In someinstances, the integrated circuit is programmed to invert (X^(T)WX) foreach cell detected by the light detection system to calculate a spectralunmixing matrix.

In certain embodiments, the integrated circuit is programmed toapproximate the inversion of (X^(T)WX) in the weighted least squarealgorithm for each cell detected in order to sort cells in the sample inreal time. In some embodiments, the integrated circuit is configured toinvert (X^(T)WX) by approximating (X^(T)WX) using an iterativeNewton-Raphson calculation according to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

where W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system. Insome embodiments, the integrated circuit is programmed to furtherestimate the variance of each photodetector. In certain instances, theintegrated circuit is programmed with an estimate of the photodetectornoise components based on a single stain control sample. In otherinstances, the variance of each photodetector is programmed to theintegrated circuit before the sample is irradiated with a light source.In still other instances, the predetermined approximation of Win theiterative Newton-Raphson calculation, W_(G), is programmed into theintegrated circuit before the sample is irradiated with a light source.In certain embodiments, the integrated circuit device is programmed toprecompute A₀ ⁻¹ with the predetermined W_(G). In these embodiments, theprecomputed A₀ ⁻¹ may be programmed into the integrated circuit deviceand used as a first approximation of the A⁻¹ for each particle detectedby the light detection system.

In other embodiments, integrated circuit devices of interest areprogrammed to approximate the weighted least square algorithm for eachparticle with a Sherman-Morrison iterative inverse updater. In someinstances, the integrated circuit device is programmed for computing Ausing the Sherman-Morrison formula:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - \frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}}$

In certain instances, the integrated circuit device is programmed forprecomputing A₀ ⁻¹ to compute the inverse of a perturbation of A₀ usingthe Sherman-Morrison formula. In some embodiments, the inverse of A₀ iscalculated by the formula X^(T)W₀X and the inverse of A is calculated bythe formula X^(T)WX. In some instances, the integrated circuit device isprogrammed to calculate ΔA (i.e., A−A₀) as a product of column vectorswith each iterative W according to:

$W_{0} = {{\begin{bmatrix}w_{11}^{0} & 0 & \ldots & 0 \\0 & w_{22}^{0} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}^{0}\end{bmatrix}\mspace{14mu}{and}\mspace{14mu} W} = \begin{bmatrix}w_{11} & 0 & \ldots & 0 \\0 & w_{22} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & w_{N_{D}N_{D}}\end{bmatrix}}$

-   -   where w_(ii)=w⁰ _(ii)+α_(i) for iϵ[1, N_(D)].

${W_{1} = {W_{0} + \begin{bmatrix}\alpha_{1} & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}},{W_{2} = {{W_{1} + \begin{bmatrix}0 & 0 & \ldots & 0 \\0 & \alpha_{2} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}}❘\mspace{14mu}{and}}}$${W = {W_{N_{D}} = {W_{N_{D} - 1} + {\begin{bmatrix}0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \alpha_{N_{D}}\end{bmatrix}\mspace{14mu}{and}}}}}\mspace{11mu}$${\Delta\; W_{i}} = {{W_{i} - W} = \begin{bmatrix}0 & 0 & 0 & \ldots & 0 \\\vdots & \ddots & \vdots & \vdots & 0 \\0 & \ldots & \alpha_{i} & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & \ldots & 0\end{bmatrix}}$

According to embodiments, ΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) whereA can be expressed as:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

In these embodiments, each A can be recomputed from A₀ with each newweight matrix W (i.e., with different values from W₀) using the changeto each w_(i). In some embodiments, the integrated circuit device isprogrammed to perform a Sherman-Morrison iterative inverse updater forapproximating the spectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

In some embodiments, a precomputed value for A₀ ⁻¹ is used to calculateA₁ ⁻¹. The precomputed A₁ ⁻¹ is then used to calculate A₂ ⁻¹. The valueA⁻¹ can be calculated by repeat computing of A_(i) ⁻¹ using each(A_(i−1))⁻¹ from i=1 to N_(D).

In other embodiments, integrated circuit devices of interest areprogrammed to calculate the weighted least square algorithm for eachparticle by matrix decomposition. In some instances, the integratedcircuit device is programmed for instructions for a LU matrixdecomposition, such as where a matrix is decomposed into a product of alower-triangular (L) matrix and an upper-triangular (U) matrix. Incertain instances, LU decomposition includes Gaussian elimination. Inother instances, LU decomposition includes a modified Choleskydecomposition, an LDL decomposition where D is diagonal matrix. Incertain embodiments, integrated circuit devices are programmed tocalculate the weighted least squares algorithm (a) using a modifiedCholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B LDL decomposition

Lz=B where z=DL ^(T) a Lower-triangular matrix solution

Dx=z where x=L ^(T) a Diagonal matrix solution

L ^(T) a=x Upper-triangular matrix solution

In other embodiments, integrated circuit devices are programmed tocalculate a weighted least squares algorithm by QR factorization. Insome instances, the QR factorization is a matrix that is the product ofan orthogonal (Q) matrix and an upper-triangular (R) matrix. In someembodiments, integrated circuit devices are programmed to calculate theweighted least squares algorithm (a) using QR factorization accordingto:

X^(T)WXa=X^(T)Wy

X ^(T) Xa=X ^(T) y where QR=X (QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

In yet other embodiments, integrated circuit devices are programmed tocalculate a weighted least squares algorithm by singular valuedecomposition (SVD). In some instances, the singular value decompositionis the matrix that is the product X=UΣV^(T) where U and V are orthogonalmatrices and Z is a diagonal matrix containing singular values of X. Incertain instances, integrated circuit devices are programmed tocalculate the weighted least squares algorithm (a) using singular valuedecomposition according to:

z=U ^(T) y

Σw=z

a=Vw

In some embodiments, integrated circuits of interest are programmed tocalculate the abundance of one or more fluorophores in the sample fromthe spectrally resolved light from each fluorophore. In certaininstances, the abundance of fluorophores associated with (e.g.,chemically associated (i.e., covalently, ionically) or physicallyassociated) a target particle is calculated from the spectrally resolvedlight from each fluorophore associated with the particle. For instance,in one example the integrated circuit is programmed to calculate therelative abundance of each fluorophore associated with a target particlefrom the spectrally resolved light from each fluorophore. In anotherexample, the integrated circuit is programmed to calculate the absoluteabundance of each fluorophore associated with the target particle fromthe spectrally resolved light from each fluorophore.

In certain embodiments, the integrated circuit is programmed to identifyor classify a particle based on the relative abundance of eachfluorophore determined to be associated with the particle. In theseembodiments, the integrated circuits may be programmed to identify orclassify the particle by any convenient protocol such as by: comparingthe relative or absolute abundance of each fluorophore associated with aparticle with a control sample having particles of known identity; or byconducting spectroscopic or other assay analysis of a population ofparticles (e.g., cells) having the calculated relative or absoluteabundance of associated fluorophores.

Kits

Aspects of the present disclosure further include kits, where kitsinclude one or more of the integrated circuits described herein. In someembodiments, kits may further include programming for the subjectsystems, such as in the form of a computer readable medium (e.g., flashdrive, USB storage, compact disk, DVD, Blu-ray disk, etc.) orinstructions for downloading the programming from an internet webprotocol or cloud server. Kits may further include instructions forpracticing the subject methods. These instructions may be present in thesubject kits in a variety of forms, one or more of which may be presentin the kit. One form in which these instructions may be present is asprinted information on a suitable medium or substrate, e.g., a piece orpieces of paper on which the information is printed, in the packaging ofthe kit, in a package insert, and the like. Yet another form of theseinstructions is a computer readable medium, e.g., diskette, compact disk(CD), portable flash drive, and the like, on which the information hasbeen recorded. Yet another form of these instructions that may bepresent is a website address which may be used via the internet toaccess the information at a removed site.

Utility

The subject systems, methods and computer systems find use in a varietyof applications where it is desirable to analyze and sort particlecomponents in a sample in a fluid medium, such as a biological sample.In some embodiments, the systems and methods described herein find usein flow cytometry characterization of biological samples labelled withfluorescent tags. In other embodiments, the systems and methods find usein spectroscopy of emitted light. In addition, the subject systems andmethods find use in increasing the obtainable signal from lightcollected from a sample (e.g., in a flow stream). In certain instances,the present disclosure finds use in enhancing measurement of lightcollected from a sample that is irradiated in a flow stream in a flowcytometer. Embodiments of the present disclosure find use where it isdesirable to provide a flow cytometer with improved cell sortingaccuracy, enhanced particle collection, particle charging efficiency,more accurate particle charging and enhanced particle deflection duringcell sorting.

Embodiments of the present disclosure also find use in applicationswhere cells prepared from a biological sample may be desired forresearch, laboratory testing or for use in therapy. In some embodiments,the subject methods and devices may facilitate obtaining individualcells prepared from a target fluidic or tissue biological sample. Forexample, the subject methods and systems facilitate obtaining cells fromfluidic or tissue samples to be used as a research or diagnosticspecimen for diseases such as cancer. Likewise, the subject methods andsystems may facilitate obtaining cells from fluidic or tissue samples tobe used in therapy. Methods and devices of the present disclosure allowfor separating and collecting cells from a biological sample (e.g.,organ, tissue, tissue fragment, fluid) with enhanced efficiency and lowcost as compared to traditional flow cytometry systems.

Aspects, including embodiments, of the subject matter described hereinmay be beneficial alone or in combination, with one or more otheraspects or embodiments. Without limiting the description, certainnon-limiting aspects of the disclosure numbered 1-320 are providedbelow. As will be apparent to those of skill in the art upon readingthis disclosure, each of the individually numbered aspects may be usedor combined with any of the preceding or following individually numberedaspects. This is intended to provide support for all such combinationsof aspects and is not limited to combinations of aspects explicitlyprovided below:

1. A method comprising:

detecting light with a light detection system from a sample comprising aplurality of fluorophores having overlapping fluorescence spectra; and

spectrally resolving light from each fluorophore in the sample.

2. The method according to 1, wherein the fluorescence spectra of eachfluorophore overlaps with the fluorescence spectra of at least one otherfluorophore in the sample.3. The method according to 2, wherein the fluorescence spectra of eachfluorophore overlaps with the fluorescence spectra of at least one otherfluorophore in the sample by 10 nm or more.4. The method according to 2, wherein the fluorescence spectra of eachfluorophore overlaps with the fluorescence spectra of at least one otherfluorophore in the sample by 25 nm or more.5. The method according to 1, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample.6. The method according to 5, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample by 10 nm or more.7. The method according to 5, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample by 25 nm or more.8. The method according to any one of 1-7, wherein spectrally resolvinglight from each fluorophore comprises calculating a spectral unmixingmatrix for the fluorescence spectra of each fluorophore in the sample.9. The method according to 8, wherein the method comprises calculatingthe spectral unmixing matrix using a weighted least squares algorithm.10. The method according to 9, wherein the weighted least squaresalgorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

â is estimated fluorophore abundance;

X is spillover; and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

11. The method according to 10, wherein each W_(ii) is calculatedaccording to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

12. The method according to any one of 9-11, wherein the methodcomprises calculating the spectral unmixing matrix according to:

(X ^(T) WX)⁻¹ X ^(T) W

13. The method according to any one of 9-11, wherein the methodcomprises inverting (X^(T)WX) for each cell to calculate the spectralunmixing matrix.14. The method according to 13, wherein inverting (X^(T)WX) comprisesapproximating (X^(T)WX) using an iterative Newton-Raphson calculationaccording to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system.

15. The method according to 14, further comprising determining W_(G)before irradiating the sample with the light source.16. The method according to 15, further comprising precomputing A₀ ⁻¹with the calculated W_(G) value.17. The method according to any one of 9-13, wherein the methodcomprises approximating (X^(T)WX) using a Sherman-Morrison iterativeinverse updater according to:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

18. The method according to 17, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

19. The method according to 18, further comprising approximating thespectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

20. The method according to 19, wherein a precomputed value for A₀ ⁻¹ isused to calculate A₁ ⁻¹ and A⁻¹ is calculated by repeat computing ofA_(i) ⁻¹ using each (A_(i−1))⁻¹ from i=1 to N_(D).21. The method according to any one of 9-13, wherein the weighted leastsquares algorithm is calculated by matrix decomposition.22. The method according to 21, wherein the matrix decompositioncomprises LU decomposition.23. The method according to 22, wherein the weighted least squaresalgorithm is calculated using a modified Cholesky decompositionaccording to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Dx=z where x=L ^(T) a

L ^(T) a=x

24. The method according to 21, wherein the weighted least squaresalgorithm is calculated by QR factorization.25. The method according to 24, wherein the weighted least squaresalgorithm is calculated using QR factorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

26. The method according to 21, wherein the weighted least squaresalgorithm is calculated by singular value decomposition.27. The method according to 26, wherein the weighted least squaresalgorithm is calculated using singular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Z is a diagonal matrixcontaining singular values of X.

28. The method according to any one of 13-27, wherein the spectralunmixing matrix is calculated on a field programmable gated array.29. The method according to any one of 1-28, further comprisingirradiating the sample with a light source.30. The method according to 29, wherein the light source comprises alaser.31. The method according to 30, wherein the light source comprises aplurality of lasers.32. The method according to any one of 1-31, wherein the light detectionsystem comprises a plurality of photodetectors.33. The method according to 32, wherein the photodetectors comprise oneor more photomultiplier tubes.34. The method according to any one of 1-31, wherein the light detectionsystem comprises a photodetector array.35. The method according to 34, wherein the photodetector arraycomprises photodiodes.36. The method according to 34, wherein the photodetector arraycomprises charge coupled devices.37. A system comprising:

a light source configured to irradiate a sample comprising a pluralityof fluorophores having overlapping fluorescence spectra;

a light detection system comprising a plurality of photodetectors; and

a processor comprising memory operably coupled to the processor whereinthe memory comprises instructions stored thereon, which when executed bythe processor, cause the processor to spectrally resolve light from eachfluorophore in the sample.

38. The system according to 37, wherein the fluorescence spectra of eachfluorophore overlaps with the fluorescence spectra of at least one otherfluorophore in the sample.39. The system according to 38, wherein the fluorescence spectra of eachfluorophore overlaps with the fluorescence spectra of at least one otherfluorophore in the sample by 10 nm or more.40. The system according to 38, wherein the fluorescence spectra of eachfluorophore overlaps with the fluorescence spectra of at least one otherfluorophore in the sample by 25 nm or more.41. The system according to 37, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample.42. The system according to 41, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample by 10 nm or more.43. The system according to 41, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample by 25 nm or more.44. The system according to any one of 37-43, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to calculate a spectral unmixing matrixfor the fluorescence spectra of each fluorophore in the sample.45. The system according to 44, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the spectral unmixing matrix by a weightedleast squares algorithm.46. The system according to 45, wherein the weighted least squaresalgorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

â is estimated fluorophore abundance;

X is spillover; and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

47. The system according to 46, wherein each W_(ii) is calculatedaccording to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

48. The system according to any one of 45-47, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to calculate the spectral unmixing matrixaccording to:

(X ^(T) WX)⁻¹ X ^(T) W

49. The system according to 48, wherein (X^(T)WX) is inverted for eachcell detected by the light detection system to calculate a spectralunmixing matrix.50. The system according to 49, wherein the inversion of (X^(T)WX) isapproximated using an iterative Newton-Raphson calculation according to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system.

51. The system according to 50, wherein variance of the photodetectorcomprises a photodetector noise component.52. The system according to 51, wherein the photodetector noisecomponent comprises one or more of electronic noise and opticalbackground light.53. The system according to any one of 51-52, wherein variance of thephotodetector is proportional to measured intensity of light by thephotodetector.54. The system according to any one of 51-53, wherein the photodetectornoise component is estimated using a single stain control sample.55. The system according to any one of 51-54, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to automatically determine the varianceof each photodetector before irradiating the sample with the lightsource.56. The system according to any one of 51-55, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to automatically determine W_(G) beforeirradiating the sample with the light source.57. The system according to 56, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate A₀ ⁻¹ based on the determined W_(G) value.58. The system according to any one of 44-49, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to approximate (X^(T)WX) using aSherman-Morrison iterative inverse updater according to:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

59. The system according to 58, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

60. The system according to 59, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to approximate the spectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

61. The system according to 60, wherein a precomputed value for A₀ ⁻¹ isused to calculate A₁ ⁻¹ and A⁻¹ is calculated by repeat computing ofA_(i) ⁻¹ using each (A_(i−1))⁻¹ from i=1 to N_(D).62. The system according to any one of 44-49, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to calculate the weighted least squaresalgorithm by matrix decomposition.63. The system according to 62, wherein the matrix decompositioncomprises LU decomposition.64. The system according to 63, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm using amodified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Lz=B where z=DL ^(T) a

L ^(T) a=x

65. The system according to 62, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm by QRfactorization.66. The system according to 65, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm using QRfactorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

67. The system according to 62, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm bysingular value decomposition.68. The system according to 67, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm usingsingular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Z is a diagonal matrixcontaining singular values of X.

69. The system according to any one of 37-68, wherein the spectralunmixing matrix is calculated on a field programmable gated array.70. The system according to any one of 37-69, wherein the light sourcecomprises a laser.71. The system according to 70, wherein the light source comprises aplurality of lasers.72. The system according to any one of 37-71, wherein the lightdetection system comprises photomultiplier tubes.73. The system according to any one of 37-72, wherein the lightdetection system comprises a photodetector array.74. The system according to 73, wherein the photodetector arraycomprises photodiodes.75. The system according to 74, wherein the photodetector arraycomprises charge coupled devices.76. An integrated circuit programmed to spectrally resolve light fromeach fluorophore in the sample comprising a plurality of fluorophoreshaving overlapping fluorescence spectra.77. The integrated circuit according to 76, wherein the fluorescencespectra of each fluorophore overlaps with the fluorescence spectra of atleast one other fluorophore in the sample.78. The integrated circuit according to 77, wherein the fluorescencespectra of each fluorophore overlaps with the fluorescence spectra of atleast one other fluorophore in the sample by 10 nm or more.79. The integrated circuit according to 77, wherein the fluorescencespectra of each fluorophore overlaps with the fluorescence spectra of atleast one other fluorophore in the sample by 25 nm or more.80. The integrated circuit according to 76, wherein the fluorescencespectra of at least one fluorophore in the sample overlaps with thefluorescence spectra of two different fluorophores in the sample.81. The integrated circuit according to 80, wherein the fluorescencespectra of at least one fluorophore in the sample overlaps with thefluorescence spectra of two different fluorophores in the sample by 10nm or more.82. The integrated circuit according to 80, wherein the fluorescencespectra of at least one fluorophore in the sample overlaps with thefluorescence spectra of two different fluorophores in the sample by 25nm or more. 83. The integrated circuit according to any one of 76-82,wherein the integrated circuit is programmed to calculate a spectralunmixing matrix for the fluorescence spectra of each fluorophore in thesample.84. The integrated circuit according to 83, wherein the integratedcircuit is programmed to calculate the spectral unmixing matrix by aweighted least squares algorithm.85. The integrated circuit according to 84, wherein the weighted leastsquares algorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

â is estimated fluorophore abundance;

X is spillover; and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

86. The integrated circuit according to 85, wherein each W_(ii) iscalculated according to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

87. The integrated circuit according to any one of 84-86, wherein theintegrated circuit is programmed to calculate the spectral unmixingmatrix according to:

(X ^(T) WX)⁻¹ X ^(T) W

88. The integrated circuit according to 87, wherein (X^(T)WX) isinverted for each cell detected by the light detection system tocalculate a spectral unmixing matrix.89. The integrated circuit according to 88, wherein the inversion of(X^(T)WX) is approximated using an iterative Newton-Raphson calculationaccording to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in a light detection system fordetecting fluorescence from the fluorophores in the sample.

90. The integrated circuit according to 89, wherein the integratedcircuit is programmed to automatically determine W_(G) beforeirradiating the sample with the light source.91. The integrated circuit according to 90, wherein the integratedcircuit is programmed to calculate A₀ ⁻¹ based on the determined W_(G)value.92. The integrated circuit according to any one of 83-88, wherein theintegrated circuit is programmed to approximate (X^(T)WX) using aSherman-Morrison iterative inverse updater according to:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

93. The integrated circuit according to claim 92, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

94. The integrated circuit according to 93, wherein the integratedcircuit is programmed to approximate the spectral unmixing matrixaccording to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

95. The integrated circuit according to 94, wherein a precomputed valuefor A₀ ⁻¹ is used to calculate A₁ ⁻¹ and A⁻¹ is calculated by repeatcomputing of A_(i) ⁻¹ using each (A_(i−1))⁻¹ from i=1 to N_(D).96. The integrated circuit according to 84, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmby matrix decomposition.97. The integrated circuit according to 96, wherein the matrixdecomposition comprises LU decomposition.98. The integrated circuit according to 97, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmusing a modified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Lz=B where z=DL ^(T) a

L ^(T) a=x

99. The integrated circuit according to 96, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmby QR factorization.100. The integrated circuit according to 99, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmusing QR factorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

101. The integrated circuit according to 96, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmby singular value decomposition.102. The integrated circuit according to 101, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmusing singular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Σ is a diagonal matrixcontaining singular values of {circumflex over (X)}.

103. The integrated circuit according to any one of 76-102, wherein theintegrated circuit is a field programmable gate array (FPGA).104. The integrated circuit according to any one of claims 76-102,wherein the integrated circuit is an application specific integratedcircuit (ASIC).105. The integrated circuit according to any one of 62-102, wherein theintegrated circuit is a complex programmable logic device (CPLD).106. A method comprising:

detecting light with a light detection system from a sample comprising aplurality of fluorophores, the fluorophores having overlappingfluorescence spectra; and

estimating an abundance of one or more of the fluorophores on a particlein the sample.

107. The method according to 106, wherein the fluorescence spectra ofeach fluorophore overlaps with the fluorescence spectra of at least oneother fluorophore in the sample.108. The method according to 107, wherein the fluorescence spectra ofeach fluorophore overlaps with the fluorescence spectra of at least oneother fluorophore in the sample by 10 nm or more.109. The method according to 107, wherein the fluorescence spectra ofeach fluorophore overlaps with the fluorescence spectra of at least oneother fluorophore in the sample by 25 nm or more.110. The method according to 106, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample.111. The method according to 110, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample by 10 nm or more.112. The method according to 111, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample by 25 nm or more.113. The method according to any one of 106-112, wherein estimating theabundance of the fluorophores comprises spectrally resolving the lightfrom each fluorophore on the particle.114. The method according to 113, wherein spectrally resolving lightfrom each fluorophore comprises calculating a spectral unmixing matrixfor the fluorescence spectra of each fluorophore on the particle.115. The method according to 114, wherein the method comprisescalculating the spectral unmixing matrix using a weighted least squaresalgorithm.116. The method according to 115, wherein the weighted least squaresalgorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

ā is estimated fluorophore abundance;

X is spillover: and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

117. The method according to 116, wherein each W_(ii) is calculatedaccording to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

118. The method according to any one of 115-117, wherein the methodcomprises calculating the spectral unmixing matrix according to:

(X ^(T) WX)⁻¹ X ^(T) W

119. The method according to any one of 115-117, wherein the methodcomprises inverting (X^(T)WX) for each cell to calculate the spectralunmixing matrix.120. The method according to 119, wherein inverting (X^(T)WX) comprisesapproximating (X^(T)WX) using an iterative Newton-Raphson calculationaccording to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system.

121. The method according to 120, further comprising determining W_(G)before irradiating the sample with the light source.122. The method according to 121, further comprising precomputing A₀ ⁻¹with the calculated W_(G) value.123. The method according to any one of 114-119, wherein the methodcomprises approximating (X^(T)WX) using a Sherman-Morrison iterativeinverse updater according to:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

124. The method according to 123, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

125. The method according to 124, further comprising approximating thespectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

126. The method according to 125, wherein a precomputed value for A₀ ⁻¹is used to calculate A_(i) ⁻¹ land A⁻¹ is calculated by repeat computingof Ail using each (A_(i−1))⁻¹ from i=1 to N_(D).127. The method according to any one of 114-119, wherein the weightedleast squares algorithm is calculated by matrix decomposition.128. The method according to 127, wherein the matrix decompositioncomprises LU decomposition.129. The method according to 128, wherein the weighted least squaresalgorithm is calculated using a modified Cholesky decompositionaccording to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Lz=B where z=DL ^(T) a

L ^(T) a=x

130. The method according to 127, wherein the weighted least squaresalgorithm is calculated by QR factorization.131. The method according to 130, wherein the weighted least squaresalgorithm is calculated using QR factorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

132. The method according to 131, wherein the weighted least squaresalgorithm is calculated by singular value decomposition.133. The method according to 132, wherein the weighted least squaresalgorithm is calculated using singular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Z is a diagonal matrixcontaining singular values of X.

134. The method according to any one of 114-133, wherein the spectralunmixing matrix is calculated on a field programmable gated array.135. The method according to any one of 106-134, further comprisingidentifying the particle in the sample based on the estimated abundanceof each fluorophore on the particle.136. The method according to any one of 106-135, wherein the particle isa cell.137. The method according to any one of 106-136, wherein eachfluorophore is conjugated to a biomolecule.138. The method according to 137, wherein the biomolecule is a compoundselected from the group consisting of a polypeptide, a nucleic acid anda polysaccharide.139. The method according to any one of 135-138, further comprisingsorting the particle based on the estimated abundance of eachfluorophore on the particle.140. The method according to any one of 106-139, further comprisingirradiating the sample with a light source.141. The method according to 140, wherein the light source comprises alaser.142. The method according to 141, wherein the light source comprises aplurality of lasers.143. The method according to any one of 106-142, wherein the lightdetection system comprises a plurality of photodetectors.144. The method according to 143, wherein the photodetectors compriseone or more photomultiplier tubes.145. The method according to any one of 106-142, wherein the lightdetection system comprises a photodetector array.146. The method according to 145, wherein the photodetector arraycomprises photodiodes.147. The method according to 146, wherein the photodetector arraycomprises charge coupled devices.148. A system comprising:

a light source configured to irradiate a sample comprising a pluralityof fluorophores having overlapping fluorescence spectra;

a light detection system comprising a plurality of photodetectors; and

a processor comprising memory operably coupled to the processor whereinthe memory comprises instructions stored thereon, which when executed bythe processor, cause the processor to estimate an abundance of one ormore of the fluorophores on a particle in the sample.

149. The system according to 148, wherein the fluorescence spectra ofeach fluorophore overlaps with the fluorescence spectra of at least oneother fluorophore in the sample.150. The system according to 149, wherein the fluorescence spectra ofeach fluorophore overlaps with the fluorescence spectra of at least oneother fluorophore in the sample by 10 nm or more.151. The system according to 149, wherein the fluorescence spectra ofeach fluorophore overlaps with the fluorescence spectra of at least oneother fluorophore in the sample by 25 nm or more.152. The system according to 148, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample.153. The system according to 152, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample by 10 nm or more.154. The system according to 152, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample by 25 nm or more.155. The system according to any one of 148-154, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to estimate the abundance of thefluorophores by spectrally resolving the light from each fluorophore onthe particle.156. The system according to 155, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate a spectral unmixing matrix for thefluorescence spectra of each fluorophore in the sample.157. The system according to 156, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the spectral unmixing matrix by a weightedleast squares algorithm.158. The system according to 157, wherein the weighted least squaresalgorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

ā is estimated fluorophore abundance;

X is spillover: and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

159. The system according to 158, wherein each W_(ii) is calculatedaccording to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

160. The system according to any one of 157-159, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to calculate the spectral unmixing matrixaccording to:

(X ^(T) WX)⁻¹ X ^(T) W

161. The system according to 160, wherein (X^(T)WX) is inverted for eachcell detected by the light detection system to calculate a spectralunmixing matrix.162. The system according to 161, wherein the inversion of (X^(T)WX) isapproximated using an iterative Newton-Raphson calculation according to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system.

163. The system according to 162, wherein variance of the photodetectorcomprises a photodetector noise component.164. The system according to 163, wherein the photodetector noisecomponent comprises one or more of electronic noise and opticalbackground light.165. The system according to any one of 163-164, wherein variance of thephotodetector is proportional to measured intensity of light by thephotodetector.166. The system according to any one of 163-164, wherein thephotodetector noise component is estimated using a single stain controlsample.167. The system according to any one of 165-166, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to automatically determine the varianceof each photodetector before irradiating the sample with the lightsource.168. The system according to any one of 164-167, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to automatically determine W_(G) beforeirradiating the sample with the light source.169. The system according to 168, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate A₀ ⁻¹ based on the determined W_(G) value.170. The system according to any one of 156-161, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to approximate (X^(T)WX) using aSherman-Morrison iterative inverse updater according to:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

171. The system according to claim 170, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

172. The system according to 171, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to approximate the spectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

173. The system according to 172, wherein a precomputed value for A₀ ⁻¹is used to calculate A₁ ⁻¹ land A⁻¹ is calculated by repeat computing ofA_(i) ⁻¹ using each (A_(i−1))⁻¹ from i=1 to N_(D).174. The system according to any one of 156-161, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to calculate the weighted least squaresalgorithm by matrix decomposition.175. The system according to 174, wherein the matrix decompositioncomprises LU decomposition.176. The system according to 175, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm using amodified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Lz=B where z=DL ^(T) a

L ^(T) a=x

177. The system according to 174, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm by QRfactorization.178. The system according to 177, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm using QRfactorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

179. The system according to 174, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm bysingular value decomposition.180. The system according to 179, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm usingsingular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Z is a diagonal matrixcontaining singular values of X.

181. The system according to any one of 156-180, wherein the spectralunmixing matrix is calculated on a field programmable gated array.182. The system according to any one of 148-181, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to identify the particle in the samplebased on the estimated abundance of each fluorophore on the particle.183. The system according to any one of 148-182, wherein the particle isa cell.184. The system according to any one of 148-183, wherein eachfluorophore is conjugated to a biomolecule.185. The system according to 184, wherein the biomolecule is a compoundselected from the group consisting of a polypeptide, a nucleic acid anda polysaccharide.186. The system according to any one of 182-185, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to sort the particle based on theestimated abundance of each fluorophore on the particle.187. The system according to any one of 148-186, wherein the lightsource comprises a laser.188. The system according to 187, wherein the light source comprises aplurality of lasers.189. The system according to any one of 148-188, wherein the lightdetection system comprises photomultiplier tubes.190. The system according to any one of 148-189, wherein the lightdetection system comprises a photodetector array.191. The system according to 190, wherein the photodetector arraycomprises photodiodes.192. The system according to 190, wherein the photodetector arraycomprises charge coupled devices.193. An integrated circuit programmed to estimate an abundance of one ormore of the fluorophores on a particle in a sample comprising aplurality of fluorophores having overlapping fluorescence spectra.194. The integrated circuit according to 193, wherein the fluorescencespectra of each fluorophore overlaps with the fluorescence spectra of atleast one other fluorophore in the sample.195. The integrated circuit according to 194, wherein the fluorescencespectra of each fluorophore overlaps with the fluorescence spectra of atleast one other fluorophore in the sample by 10 nm or more.196. The integrated circuit according to 194, wherein the fluorescencespectra of each fluorophore overlaps with the fluorescence spectra of atleast one other fluorophore in the sample by 25 nm or more.197. The integrated circuit according to 193, wherein the fluorescencespectra of at least one fluorophore in the sample overlaps with thefluorescence spectra of two different fluorophores in the sample.198. The integrated circuit according to 197, wherein the fluorescencespectra of at least one fluorophore in the sample overlaps with thefluorescence spectra of two different fluorophores in the sample by 10nm or more.199. The integrated circuit according to 197, wherein the fluorescencespectra of at least one fluorophore in the sample overlaps with thefluorescence spectra of two different fluorophores in the sample by 25nm or more.200. The integrated circuit according to any one of 193-199, wherein theintegrated circuit is programmed to estimate the abundance of thefluorophores by spectrally resolving the light from each fluorophore onthe particle.201. The integrated circuit according to any one of 193-199, wherein theintegrated circuit is programmed to calculate a spectral unmixing matrixfor the fluorescence spectra of each fluorophore in the sample.202. The integrated circuit according to 201, wherein the integratedcircuit is programmed to calculate the spectral unmixing matrix by aweighted least squares algorithm.203. The integrated circuit according to 202, wherein the weighted leastsquares algorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

ā is estimated fluorophore abundance;

X is spillover; and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

204. The integrated circuit according to 202, wherein each W_(ii) iscalculated according to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

205. The integrated circuit according to any one of 202-204, wherein theintegrated circuit is programmed to calculate the spectral unmixingmatrix according to:

(X ^(T) WX)⁻¹ X ^(T) W

206. The integrated circuit according to 205, wherein (X^(T)WX) isinverted for each cell detected by the light detection system tocalculate a spectral unmixing matrix.207. The integrated circuit according to 205, wherein the inversion of(X^(T)WX) is approximated using an iterative Newton-Raphson calculationaccording to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in a light detection system fordetecting fluorescence from the fluorophores in the sample.

208. The integrated circuit according to 207, wherein the integratedcircuit is programmed to automatically determine W_(G) beforeirradiating the sample with the light source.209. The integrated circuit according to 208, wherein the integratedcircuit is programmed to calculate A₀ ⁻¹ based on the determined W_(G)value.210. The integrated circuit according to any one of 201-206, wherein theintegrated circuit is programmed to approximate (X^(T)WX) using aSherman-Morrison iterative inverse updater according to:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

211. The integrated circuit according to 210, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

212. The integrated circuit according to 211, wherein the integratedcircuit is programmed to approximate the spectral unmixing matrixaccording to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

213. The integrated circuit according to 212, wherein a precomputedvalue for A₀ ⁻¹ is used to calculate A₁ ⁻¹ and A⁻¹ is calculated byrepeat computing of A_(i) ⁻¹ using each (A_(i−1))⁻¹ from i=1 to N_(D).214. The integrated circuit according to any one of 201-206, wherein theintegrated circuit is programmed to calculate the weighted least squaresalgorithm by matrix decomposition.215. The integrated circuit according to 214, wherein the matrixdecomposition comprises LU decomposition.216. The integrated circuit according to 215, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmusing a modified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Lz=B where z=DL ^(T) a

L ^(T) a=x

217. The integrated circuit according to 214, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmby QR factorization.218. The integrated circuit according to 217, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmusing QR factorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

219. The integrated circuit according to 218, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmby singular value decomposition.220. The integrated circuit according to 219, wherein the integratedcircuit is programmed to calculate the weighted least squares algorithmusing singular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Z is a diagonal matrixcontaining singular values of X.

221. The integrated circuit according to any one of 193-220, wherein theintegrated circuit is programmed to identify the particle in the samplebased on the estimated abundance of each fluorophore on the particle.222. The integrated circuit according to 221, wherein the integratedcircuit is programmed to sort the particle based on the estimatedabundance of each fluorophore on the particle.223. The integrated circuit according to any one of 193-222, wherein theintegrated circuit is a field programmable gate array (FPGA).224. The integrated circuit according to any one of 193-222, wherein theintegrated circuit is an application specific integrated circuit (ASIC).225. The integrated circuit according to any one of 193-222, wherein theintegrated circuit is a complex programmable logic device (CPLD).226. A system comprising:

a light source configured to irradiate a sample comprising a pluralityof fluorophores;

a light detection system comprising a plurality of photodetectors; and

a processor comprising memory operably coupled to the processor whereinthe memory comprises instructions stored thereon, which when executed bythe processor, cause the processor to:

-   -   calculate a spectral unmixing matrix for the fluorescence        spectra of the plurality of fluorophores for each cell detected        by the light detection system; and    -   estimate the abundance of each fluorophore using the spectral        unmixing matrix; and

a cell sorting component that is configured to sort cells in the samplebased on the estimated fluorophore abundance.

227. The system according to 226, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the spectral unmixing matrix by a weightedleast squares algorithm.228. The system according to 227, wherein the weighted least squaresalgorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

â is estimated fluorophore abundance;

X is spillover; and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{i + 1,i + 1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

229. The system according to 228, wherein each W_(ii) is calculatedaccording to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

230. The system according to 228, wherein the spectral unmixing matrixis calculated according to:

(X ^(T) WX)⁻¹ X ^(T) W

231. The system according to 228, wherein (X^(T)WX) is inverted for eachcell detected by the light detection system to calculate a spectralunmixing matrix.232. The system according to 231, wherein the inversion of (X^(T)WX) isapproximated using an iterative Newton-Raphson calculation according to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system.

233. The system according to 232, wherein variance of the photodetectorcomprises a photodetector noise component.234. The system according to 233, wherein the photodetector noisecomponent comprises one or more of electronic noise and opticalbackground light.235. The system according to any one of 233-234, wherein variance of thephotodetector is proportional to measured intensity of light by thephotodetector.236. The system according to any one of 233-235, wherein thephotodetector noise component is estimated using a single stain controlsample.237. The system according to any one of 233-236, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to automatically determine the varianceof each photodetector before irradiating the sample with the lightsource.238. The system according to any one of 232-237, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to automatically determine W_(G) beforeirradiating the sample with the light source.239. The system according to 238, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate A₀ ⁻¹ based on the determined W_(G) value.240. The system according to 239, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate A₀ ⁻¹ based on the determined W_(G) value.241. The system according to any one of 227-231, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to approximate (X^(T)WX) using aSherman-Morrison iterative inverse updater according to:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

242. The system according to 241, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

243. The system according to 242, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to approximate the spectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

244. The system according to 243, wherein a precomputed value for A₀ ⁻¹is used to calculate A₁ ⁻¹ and A⁻¹ is calculated by repeat computing ofA_(i) ⁻¹ using each (A_(i−1))⁻¹ from i=1 to N_(D).245. The system according to any one of 227-231, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to calculate the weighted least squaresalgorithm by matrix decomposition.246. The system according to 245, wherein the matrix decompositioncomprises LU decomposition.247. The system according to 246, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm using amodified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Lz=B where z=DL ^(T) a

L ^(T) a=x

248. The system according to 245, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm by QRfactorization.249. The system according to 248, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm using QRfactorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

250. The system according to 245, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm bysingular value decomposition.251. The system according to 250, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm usingsingular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Z is a diagonal matrixcontaining singular values of X.

252. The system according to any one of 226-251, wherein the spectralunmixing matrix is calculated on a field programmable gated array.253. The system according to any one of 226-252, wherein the lightsource comprises a laser.254. The system according to 253, wherein the light source comprises aplurality of lasers.255. The system according to any one of 226-254, wherein the lightdetection system comprises photomultiplier tubes.256. The system according to any one of 226-255, wherein the lightdetection system comprises a photodetector array.257. The system according to 256, wherein the photodetector arraycomprises photodiodes.258. The system according to 256, wherein the photodetector arraycomprises charge coupled devices.259. The system according to any one of 226-258, wherein the cellsorting component comprises a droplet deflector.260. The system according to any one of 226-259, wherein the systemfurther comprises:

a flow cell nozzle comprising an orifice; and

a sample interrogation region in fluid communication with the flow cellnozzle orifice for irradiating the sample with the light source.

261. The system according to 260, further comprising a cuvettepositioned in the sample interrogation region.262. A method for sorting cells of a sample, the method comprising:

detecting light emitted from a sample comprising a plurality offluorophores with a light detection system comprising a plurality ofphotodetectors;

calculating a spectral unmixing matrix for the fluorescence spectra ofthe plurality of fluorophores for each cell detected by the lightdetection system;

estimating the abundance of each fluorophore using the spectral unmixingmatrix; and

sorting cells in the sample based on the estimated fluorophoreabundance.

263. The method according to 262, wherein the method comprisescalculating the spectral unmixing matrix using a weighted least squaresalgorithm.264. The method according to 263, wherein the weighted least squaresalgorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

â is estimated fluorophore abundance;

X is spillover; and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{{i + 1},{i + 1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

265. The method according to 264, wherein each W_(ii) is calculatedaccording to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

266. The method according to 264, wherein the method comprisescalculating the spectral unmixing matrix according to:

(X ^(T) WX)⁻¹ X ^(T) W

267. The method according to 264, wherein the method comprises inverting(X^(T)WX) for each cell detected by the light detection system tocalculate a spectral unmixing matrix.268. The method according to 267, wherein inverting (X^(T)WX) comprisesapproximating (X^(T)WX) using an iterative Newton-Raphson calculationaccording to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system.

269. The method according to 268, further comprising precomputing A₀ ⁻¹with the calculated W_(G) value.270. The method according to any one of 263-267, wherein the methodcomprises approximating (X^(T)WX) using a Sherman-Morrison iterativeinverse updater according to:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

271. The method according to 270, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

272. The method according to 271, further comprising approximating thespectral unmixing matrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

273. The method according to 272, wherein a precomputed value for A₀ ⁻¹is used to calculate A₁ ⁻¹ and A⁻¹ is calculated by repeat computing ofA_(i) ⁻¹ using each (A_(i−1))⁻¹ from i=1 to N_(D).274. The method according to any one of 263-267, wherein the weightedleast squares algorithm is calculated by matrix decomposition.275. The method according to 274, wherein the matrix decompositioncomprises LU decomposition.276. The method according to 275, wherein the weighted least squaresalgorithm is calculated using a modified Cholesky decompositionaccording to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Lz=B where z=DL ^(T) a

L ^(T) a=x

277. The method according to 274, wherein the weighted least squaresalgorithm is calculated by QR factorization.278. The method according to 277, wherein the weighted least squaresalgorithm is calculated using QR factorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

279. The method according to 274, wherein the weighted least squaresalgorithm is calculated by singular value decomposition.280. The method according to 279, wherein the weighted least squaresalgorithm is calculated using singular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Z is a diagonal matrixcontaining singular values of X.

281. The method according to 268, wherein variance of the photodetectorcomprises a photodetector noise component.282. The method according to 281, wherein the photodetector noisecomponent comprises one or more of electronic noise and opticalbackground light.283. The method according to any one of 281-282, wherein variance of thephotodetector is proportional to measured intensity of light by thephotodetector.284. The method according to any one of 281-283, further comprisingestimating the photodetector noise components using a single staincontrol sample.285. The method according to any one of 281-284, further comprisingdetermining the variance of each photodetector before irradiating thesample with the light source.286. The method according to any one of 268-285, further comprisingdetermining W_(G) before irradiating the sample with the light source.287. The method according to any one of 262-286, wherein the spectralunmixing matrix is calculated on a field programmable gated array.288. The method according to any one of 262-287, further comprisingirradiating the sample with a light source.289. The method according to 288, wherein the light source comprises alaser.290. The method according to 289, wherein the light source comprises aplurality of lasers.291. The method according to any one of 262-290, wherein emitted lightis detected with a plurality of photodetectors comprisingphotomultiplier tubes.292. The method according to any one of 262-290, wherein emitted lightis detected with a photodetector array.293. The method according to 292, wherein the photodetector arraycomprises photodiodes.294. The method according to 292, wherein the photodetector arraycomprises charge coupled devices.295. A field programmable gate array programmed to:

calculate a spectral unmixing matrix for fluorescence spectra of aplurality of fluorophores for each cell in a sample detected by a lightdetection system having a plurality of photodetectors; and

estimate the abundance of each fluorophore using the spectral unmixingmatrix.

296. The field programmable gate array according to 295, wherein thefield programmable gate array is configured to calculate the spectralunmixing matrix using a weighted least squares algorithm.297. The field programmable gate array according to 296, wherein theweighted least squares algorithm is calculated according to:

â=(X ^(T) WX)⁻¹ X ^(T) Wy

wherein:

y is measured detector values from the plurality of photodetectors ofthe light detection system for each cell;

â is estimated fluorophore abundance;

X is spillover; and

W is

$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{{i + 1},{i + 1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$

298. The field programmable gate array according to 297, wherein eachW_(ii) is calculated according to:

$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$

wherein:

σ_(i) ² is variance at detector i;

y_(i) is signal at detector i; and

λ_(i) is constant noise at detector i.

299. The field programmable gate array according to 295, wherein thefield programmable gate array is configured to calculate the spectralunmixing matrix according to:

(X ^(T) WX)⁻¹ X ^(T) W

300. The field programmable gate array according to 297, wherein thefield programmable gate array is configured to invert (X^(T)WX) for eachcell detected to calculate a spectral unmixing matrix.301. The field programmable gate array according to 300, wherein thefield programmable gate array is configured to invert (X^(T)WX) byapproximating (X^(T)WX) using an iterative Newton-Raphson calculationaccording to:

A ⁻¹=(X ^(T) WX)⁻¹;

A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹

A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹

wherein W_(G) is a predetermined approximation of W that is determinedfrom variance of each photodetector in the light detection system.

302. The field programmable gate array according to 301, wherein theintegrated circuit is programmed to automatically determine W_(G) beforeirradiating the sample with the light source.303. The field programmable gate array according to 302, wherein theintegrated circuit is programmed to calculate A₀ ⁻¹ based on thedetermined W_(G) value.304. The field programmable gate array according to any one of 296-300,wherein the field programmable gate array is programmed to approximate(X^(T)WX) using a Sherman-Morrison iterative inverse updater accordingto:

$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$

305. The field programmable gate array according to 304, whereinΔA_(i)=X^(T)ΔW_(i)X=α_(i)m_(i)m_(i) ^(T) wherein:

$\begin{matrix}{A = {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}}} & {(1)} \\{{= {A_{0} + {\sum\limits_{i = 1}^{N_{D}}{\alpha_{i}m_{i}m_{i}^{T}}}}}\mspace{439mu}} & {(2)}\end{matrix}$

306. The field programmable gate array according to 305, wherein theintegrated circuit is programmed to approximate the spectral unmixingmatrix according to:

$\begin{matrix}{A^{- 1} = \left( {A_{0} + {\sum\limits_{i = 1}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(3)} \\{= \left( {A_{0} + {\Delta\; A_{1}} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}} & {(4)} \\{{= \left( {A_{1} + {\sum\limits_{i = 2}^{N_{D}}\;{\Delta\; A_{i}}}} \right)^{- 1}},{etc},.} & {(5)} \\{A_{i}^{- 1} = \left( {A_{i - 1} + {\alpha_{i}m_{i}m_{i}^{T}}} \right)^{- 1}} & {(6)} \\{= {A_{i - 1}^{- 1} - \frac{A_{i - 1}^{- 1}\alpha_{i}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}}} & {(7)} \\{{= {A_{i - 1}^{- 1} - {\frac{\alpha_{i}}{1 + {\alpha_{i}m_{i}^{T}A_{i - 1}^{- 1}m_{i}}}A_{i - 1}^{- 1}m_{i}m_{i}^{T}A_{i - 1}^{- 1}}}}\mspace{175mu}} & {(8)}\end{matrix}$

307. The field programmable gate array according to 306, wherein aprecomputed value for A₀ ⁻¹ is used to calculate A₁ ⁻¹ and A⁻¹ iscalculated by repeat computing of A_(i) ⁻¹ using each (A_(i−1))⁻¹ fromi=1 to N_(D).308. The field programmable gate array according to any one of 296-300,wherein the integrated circuit is programmed to calculate the weightedleast squares algorithm by matrix decomposition.309. The field programmable gate array according to 308, wherein thematrix decomposition comprises LU decomposition.310. The field programmable gate array according to 309, wherein theintegrated circuit is programmed to calculate the weighted least squaresalgorithm using a modified Cholesky decomposition according to:

X ^(T) WXa=X ^(T) Wy

Aa=B

LDL ^(T) a=B

Lz=B where z=DL ^(T) a

Lz=B where z=DL ^(T) a

L ^(T) a=x

311. The field programmable gate array according to 310, wherein theintegrated circuit is programmed to calculate the weighted least squaresalgorithm by QR factorization.312. The field programmable gate array according to 311, wherein theintegrated circuit is programmed to calculate the weighted least squaresalgorithm using QR factorization according to:

X ^(T) WXa=X ^(T) Wy

X ^(T) Xa=X ^(T) y where QR=X

(QR)^(T) QRa=(QR)^(T) y

R ^(T) Q ^(T) QRa=R ^(T) Q ^(T) y

R ^(T) Ra=R ^(T) Q ^(T) y

Ra=Q ^(T) y

313. The field programmable gate array according to 312, wherein theintegrated circuit is programmed to calculate the weighted least squaresalgorithm by singular value decomposition.314. The field programmable gate array according to 313, wherein theintegrated circuit is programmed to calculate the weighted least squaresalgorithm using singular value decomposition according to:

z=U ^(T) y

Σw=z

a=Vw,

wherein U and V are orthogonal matrices and Z is a diagonal matrixcontaining singular values of X.

315. The field programmable gate array according to 301, whereinvariance of the photodetector comprises a photodetector noise component.316. The field programmable gate array according to 315, wherein thephotodetector noise component comprises one or more of electronic noiseand optical background light.317. The field programmable gate array according to any one of 295-316,wherein variance of the photodetector is proportional to measuredintensity of light by the photodetector.318. The field programmable gate array according to any one of 295-316,wherein the field programmable gate array is programmed with an estimateof the photodetector noise components based on a single stain controlsample.319. The field programmable gate array according to any one of 295-316,wherein the variance of each photodetector is programmed to the fieldprogrammable gate array before the sample is irradiated with a lightsource.320. The field programmable gate array according to any one of 295-316,wherein W_(G) is programmed to the field programmable gate array beforethe sample is irradiated with a light source.

Although the foregoing invention has been described in some detail byway of illustration and example for purposes of clarity ofunderstanding, it is readily apparent to those of ordinary skill in theart in light of the teachings of this invention that certain changes andmodifications may be made thereto without departing from the spirit orscope of the appended claims.

Accordingly, the preceding merely illustrates the principles of theinvention. It will be appreciated that those skilled in the art will beable to devise various arrangements which, although not explicitlydescribed or shown herein, embody the principles of the invention andare included within its spirit and scope. Furthermore, all examples andconditional language recited herein are principally intended to aid thereader in understanding the principles of the invention and the conceptscontributed by the inventors to furthering the art, and are to beconstrued as being without limitation to such specifically recitedexamples and conditions. Moreover, all statements herein recitingprinciples, aspects, and embodiments of the invention as well asspecific examples thereof, are intended to encompass both structural andfunctional equivalents thereof. Additionally, it is intended that suchequivalents include both currently known equivalents and equivalentsdeveloped in the future, i.e., any elements developed that perform thesame function, regardless of structure. Moreover, nothing disclosedherein is intended to be dedicated to the public regardless of whethersuch disclosure is explicitly recited in the claims.

The scope of the present invention, therefore, is not intended to belimited to the exemplary embodiments shown and described herein. Rather,the scope and spirit of present invention is embodied by the appendedclaims. In the claims, 35 U.S.C. § 112(f) or 35 U.S.C. § 112(6) isexpressly defined as being invoked for a limitation in the claim onlywhen the exact phrase “means for” or the exact phrase “step for” isrecited at the beginning of such limitation in the claim; if such exactphrase is not used in a limitation in the claim, then 35 U.S.C. § 112(f) or 35 U.S.C. § 112(6) is not invoked.

1.-20. (canceled)
 21. A system comprising: a light source configured toirradiate a sample comprising a plurality of fluorophores havingoverlapping fluorescence spectra; a light detection system comprising aplurality of photodetectors; and a processor comprising memory operablycoupled to the processor wherein the memory comprises instructionsstored thereon, which when executed by the processor, cause theprocessor to spectrally resolve light from each fluorophore in thesample using a weighted least squares algorithm that employs anestimated fluorophore abundance value.
 22. The system according to claim21, wherein the fluorescence spectra of each fluorophore overlaps withthe fluorescence spectra of at least one other fluorophore in thesample.
 23. The system according to claim 22, wherein the fluorescencespectra of each fluorophore overlaps with the fluorescence spectra of atleast one other fluorophore in the sample by 10 nm or more.
 24. Thesystem according to claim 21, wherein the fluorescence spectra of atleast one fluorophore in the sample overlaps with the fluorescencespectra of two different fluorophores in the sample.
 25. The systemaccording to claim 24, wherein the fluorescence spectra of at least onefluorophore in the sample overlaps with the fluorescence spectra of twodifferent fluorophores in the sample by 10 nm or more.
 26. The systemaccording to claim 21, wherein the memory comprises instructions storedthereon, which when executed by the processor, cause the processor tocalculate a spectral unmixing matrix for the fluorescence spectra ofeach fluorophore in the sample.
 27. The system according to claim 21,wherein the weighted least squares algorithm is calculated according to:â=(X ^(T) WX)⁻¹ X ^(T) Wy wherein: y is measured detector values fromthe plurality of photodetectors of the light detection system for eachcell; â is estimated fluorophore abundance; X is spillover; and W is$\quad\begin{bmatrix}W_{ii} & 0 & \ldots & 0 \\0 & W_{{i + 1},{i + 1}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & W_{{i + n},{i + n}}\end{bmatrix}$
 28. The system according to claim 27, wherein each Wu iscalculated according to:$W_{ii} = {\frac{1}{\sigma_{i}^{2}} \approx \frac{1}{y_{i} + \lambda_{i}}}$wherein: σ_(i) ² is variance at detector i; y_(i) is signal at detectori; and λ_(i) is constant noise at detector i.
 29. The system accordingto claim 26, wherein the memory comprises instructions stored thereon,which when executed by the processor, cause the processor to calculatethe spectral unmixing matrix according to:(X ^(T) WX)⁻¹ X ^(T) W
 30. The system according to claim 29, wherein(X^(T)WX) is inverted for each cell detected by the light detectionsystem to calculate a spectral unmixing matrix.
 31. The system accordingto 30, wherein the inversion of (X^(T)WX) is approximated using aniterative Newton-Raphson calculation according to:A ⁻¹=(X ^(T) WX)⁻¹;A ₀ ⁻¹=(X ^(T) W _(G) X)⁻¹A _(i+1) ⁻¹=(2I−A _(i) ⁻¹ A)A _(i) ⁻¹ wherein W_(G) is a predeterminedapproximation of W that is determined from variance of eachphotodetector in the light detection system.
 32. The system according toclaim 31, wherein variance of the photodetector comprises aphotodetector noise component.
 33. The system according to claim 32,wherein the photodetector noise component is estimated using a singlestain control sample.
 34. The system according to claim 30, wherein thememory comprises instructions stored thereon, which when executed by theprocessor, cause the processor to automatically determine the varianceof each photodetector before irradiating the sample with the lightsource.
 35. The system according to claim 30, wherein the memorycomprises instructions stored thereon, which when executed by theprocessor, cause the processor to automatically determine W_(G) beforeirradiating the sample with the light source.
 36. The system accordingto claim 35, wherein the memory comprises instructions stored thereon,which when executed by the processor, cause the processor to calculateA₀ ⁻¹ based on the determined W_(G) value.
 37. The system according toclaim 26, wherein the memory comprises instructions stored thereon,which when executed by the processor, cause the processor to approximate(X^(T)WX) using a Sherman-Morrison iterative inverse updater accordingto:$\left( {A_{0} + {u\; v^{T}}} \right)^{- 1} = {A_{0}^{- 1} - {\frac{A_{0}^{- 1}u\; v^{T}A_{0}^{- 1}}{1 + {v^{T}A_{0}^{- 1}u}}.}}$38. The system according to claim 26, wherein the memory comprisesinstructions stored thereon, which when executed by the processor, causethe processor to calculate the weighted least squares algorithm bymatrix decomposition.
 39. The system according to claim 26, wherein thematrix decomposition comprises LU decomposition.
 40. The systemaccording to claim 21, wherein the spectral unmixing matrix iscalculated on a field programmable gated array.